Can do a work in 15 days and B in 20 days if they work together for 4 days then the fraction of work that is left is?

A can do a work in 15 days and B in 20 days. If they together work on it for 4 days; what fraction of the work will be left?

A's 1-day work = `1/15`

B's 1-day work = `1/20`

(A+B)'s 1-day work =`1/15+1/20`

`=(4+3)/60=7/60`

(A+B)'s 4 days work =`7/60xx4=7/15`

Remaining work =`1-7/15=(15-7)/15`

`=8/15`

Is there an error in this question or solution?

Discussion :: Time and Work - General Questions (Q.No.1)

A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is :

[A].
[B].
[C].
[D].

Answer: Option D

Explanation:

A's 1 day's work =	1	;
15

B's 1 day's work =	1	;
20

(A + B)'s 1 day's work =	$Can do a work in 15 days and B in 20 days if they work together for 4 days then the fraction of work that is left is?$	1	+	1	$Can do a work in 15 days and B in 20 days if they work together for 4 days then the fraction of work that is left is?$	=	7	.
15	20	60

(A + B)'s 4 day's work =	$Can do a work in 15 days and B in 20 days if they work together for 4 days then the fraction of work that is left is?$	7	x 4	$Can do a work in 15 days and B in 20 days if they work together for 4 days then the fraction of work that is left is?$	=	7	.
60	15

Therefore, Remaining work =	$Can do a work in 15 days and B in 20 days if they work together for 4 days then the fraction of work that is left is?$	1 -	7	$Can do a work in 15 days and B in 20 days if they work together for 4 days then the fraction of work that is left is?$	=	8	.
15	15

Poorni said: (Dec 28, 2010)
Why (1 - 7/15)?

Deepa said: (Dec 29, 2010)
Can you explain how 7/60 came?

Appu said: (Dec 29, 2010)
@Deepa (1/50+1/20) = (20+15)/300 //This get by cross multiplication. = 35/300 = 7/60. I think your doubt is clear now.

Sundar said: (Dec 29, 2010)
@Poorni: The total work = 1; Work done by A and B in 4 days = 7/15. Therefore, the pending work = 1 - 7/15 = 0.533333333... (or) 8/15. Hope this help you. Have a nice day!

Beer Ibrahim said: (Dec 31, 2010)
Why (1-7/15) is applied ?

Sundar said: (Dec 31, 2010)
@Beer Ibrahim Q: Why (1-7/15) is applied ? Ans: To calculate the work remaining. Work remaining = 8/15. Note: From the above answer, we can say 15/8 days required to complete the remaining work by A and B. Hope this will help you. Have nice day!

Mohideen said: (Jan 1, 2011)
@sundar. Good explanation.

Pravin Hambire said: (Jan 26, 2011)
Can you explain how 7/60 came?

Sunny Guleria said: (Jan 30, 2011)
We have to calculate the remaining work after 4 dayz ,so why we subtract 1 dayz work from 4 day work? plz clear the question.

PRAKASH said: (Feb 6, 2011)
For A:- 15 days for 1 job in 1 day 1/15 (part of the one job) for B:- 20 days for 1 job in 1 day 1/20 (part of the one job) FOR BOTH IN ONE DAY:- 1/15+1/20=7/60 FOR BOTH IN 4 DAYS:- (7/60)*4=7/15(THEY HAVE DONE) THE REST PART OF THE JOB IS:- 1-(7/15)=8/15 (ANS)

Vishwanath said: (Feb 6, 2011)
7/60 x4 =7/15 please explain me

Well Wisher said: (Feb 10, 2011)
@Poorni: Why 1-(7/15)? We consider the total work as 1. The amount of (work done) is 7/15. Subtract the total work by the work done we will get the amount of work to be done That is why we use 1-(7/15). Hope this help you.

Malli said: (Feb 10, 2011)
@Prkash. Superb explaination.

Lottie said: (Feb 14, 2011)
I was thinking 1-7/15 will be 6/15. So how did you get 8/15. Thanx.

Analyser said: (Feb 19, 2011)
Since work done is 7/15....which is 7 parts out of 15..... So obviously total work wud be 15/15......which is 1.... Hence we subtract 7/15...from 15/15 or 1..... i.e 1-7/15.

Vijay Kumar said: (Feb 22, 2011)
Can you explain how 7/60 came ?

Sundar said: (Feb 22, 2011)
@Vijay Kumar 1/15 + 1/20 = ? 1/15 * 4/4 = 4/60 ok. 1/20 * 3/3 = 3/60 ok. Now, 4/60 + 3/60 = (4+3)/60 = 7/60. Thats all. I don't know how to explain more simpler than this. Hope you can understand this. Have a nice day!

Sheelu said: (Feb 28, 2011)
1/15+1/20=7/60 7/60*4=8/15

Sagar said: (Mar 18, 2011)
@deepa lcm of 15 and 20 is 60 so we get 7/60 understood

Amrinder said: (Mar 28, 2011)
4/60 is ok 4 is no of working and 60 is hours in day cant undestand 3/60

Rajesh Chowdary said: (Mar 29, 2011)
Explanations are good plz share any simple methods other than these

Trupti said: (Apr 25, 2011)
1-7/15 should be 6/15 please explaine how 8/15......

Parthiban said: (May 14, 2011)
@Trupti 1-7/15 = (15-7)/15 = 8/15 I hope this will help you !

Trupti said: (May 16, 2011)
Thanks Parthiban. I understood well.

Latha said: (May 23, 2011)
Why the rest part is only 1-7/15 ?

Anshuman said: (May 26, 2011)
Oh! Thanks I understood well.

Vikas said: (Jun 1, 2011)
Thanks for your explanation. But it take much time. Can you tell me tricks.

Suba said: (Jun 22, 2011)
Why we subtract with one? can you please explain.

Crompton said: (Jun 23, 2011)
Because we know that total work = 1 so we subtract with one.

Depl said: (Jun 25, 2011)
Oh! Thanks I understood well.

Sak said: (Jul 7, 2011)
1/15 * 4/4 = 4/60 ok. 1/20 * 3/3 = 3/60 ok. How do we get 4/4 and 3/3 ? Please explain.

Mani said: (Jul 13, 2011)
Still i have confusion. How 7/60 comes?

Honeymayee said: (Jul 20, 2011)
Power of a=p1=w/15 Power of b=p2=w/20 Work is same so p115=p220 p1/p2=4/3 Now I do not know how to proceed. ?

Ni333 said: (Jul 23, 2011)
Thanks analyser.

Urmm said: (Aug 1, 2011)
L.C.M. of 15 & 20 are 60 and 60/15=4 and 60/20=3 so 4+3=7 as numerator and 60 is denominator OR 1/15+1/20=[(120)+(115)]/300=(20+15)/300=35/300=7/60 35 devide by 5 and 300 devide by 5

Swetha said: (Aug 5, 2011)

We can solve this problem by another way also..let us see.. A can do a work in 15 days B can do a work in 20 days Take LCM for 15 & 20 i.e Total work = 60 Then, A's capacity = 60/15 = 4 B's capacity = 60/20 = 3 They work together for 4 days, Then, A's capacity + B's capacity = 4 + 3 =7 AB's one day capacity = 7 since they work for 4 days, they have done 4x7 =28 work Work left = Total work - work done by AB = 60 - 28 = 32 Remaining work / total work = 32 / 60 = 8 / 15

This method will take less time to compute guys...please try it.

Pradeepshne said: (Aug 6, 2011)
Wow really superb.

Sangeetha said: (Aug 6, 2011)
Yes swetha your are right. Its very simple and easy method. Thank you.

Hashir Quraishi said: (Aug 9, 2011)
Swetha you rocked.

Gowtham said: (Aug 9, 2011)
How came remaining days?

Kamal said: (Aug 13, 2011)
I didn't undestand last step.

Akanksha said: (Aug 16, 2011)
(1/50+1/20) = (20+15)/300 //This get by cross multiplication. = 35/300 = 7/60. How did 300 came?

Neha Garg said: (Sep 12, 2011)
Let total work is 1 1/15+1/20=x/4 7/60*4=x that means x=7/15 1-7/15=8/15

Fouzia said: (Sep 12, 2011)
Fouzia. How that 7 came I can't got it?

SRI HARSHA.P said: (Sep 17, 2011)
The way said by swetha is very long process. that wastes time in the exam hall. thats not the good way to do the problem. always prepare for ashort method. Short method takes time for the first time by practice it gives u TIME MANAGEMENT. So better to practice SM.

Ramkumar said: (Sep 18, 2011)
Nice work swetha.

Swetha said: (Sep 28, 2011)
@Sri harsha.p It is not very long process..it is short method only.i explained every steps.,so only it looks like long process.

Rahul said: (Oct 8, 2011)
Ok. I guess the easier way to explain this is to subtract(20days-14days)= 5 days, We have calculated for 4 days, therfore remaining is 1;)

James said: (Oct 17, 2011)
We can solve this problem more easily by taking efficiency. Since work=efficiency time To take efficiency take lcm of A&B.it is 60 60/15=4 60/20=3 A'efficiency=4 & B's=3 Work=415 or 320 =60 Work=60 Since a b works together for 4 days a+b effi=4+3=7 74=28 Total work-work done 60-28=32(work remaining) 32/60=8/15.

Ghhhhgh said: (Oct 29, 2011)
Here it is given that A can do a piece of work in 15 days. So now we can find the A's 1 day work whicvh is =1/15.

Santosh said: (Oct 29, 2011)

@Pravin Hambire Q. How 7/60 came ? See 1/15 +1/20 Now find the lcm of 15 and 20, it is 60. Now if you divide 60 by 15 quotient is 4. So mulitply 1/15 with 4, it will become 4/15 . Again divide 60 by 20. Quotient is 3, now multiply 1/20 with 3. It will become 3/20. Now you alredy know that lcm of 15 nd 20 is 60. So write 60 in denominator. Now add the quotient which is 3 nd 4 and write it in numerator. So finally 7/60 .

Hope you got it.

Vinod said: (Nov 2, 2011)
Any one can explain me why we using remaining work 1-7/15 please.

Niruban said: (Nov 16, 2011)
A does the work for a day and B does it for a same day. If we add both then it should be work done for 2 days but why is it considered as one day work?

Sunil said: (Nov 29, 2011)
How that 60 came I can't got it?

Ram said: (Dec 6, 2011)
Hi friends.......... A can do wrk in 15 dayz ; b Can do wrk in 20 dayz; then LCM of A&B=7/60; Explain: =1/15+1/20 =[(4/415)+(3/320)] =(4/60)+(3/60) =3+4/60 =7/60 If A and B do wrk in 4 day=(7/60 *4 ) =7/15 work is 1 so=1-7/15 =15-7/15 Ans is = 8/15 Its easy for ur understanding...............

Santhi said: (Dec 30, 2011)
Good explanation swetha.

Bandna said: (Jan 18, 2012)
Good shweta.

Sai Kishore said: (Jan 26, 2012)
Still I have confusion. How 7/60 comes?

Razeena said: (Jan 27, 2012)

Hi friends, A's 1 day work=1/15; B's 1 day work=1/20 OK.Then we calculate how much A + B can do in 1 day. ie 1/15 + 1/20 ( in fraction if denominator is different first we find the l.c.m of denominator).so we calculate the l.c.m of 15 and 20 ie 60(15 and 20 is divided by 5 we get the answer 3 and 4 so we find l.c.m by multiplying 5*3*4=60).1/15*60+1/20*60=4+3/60=7/60. if A and B do work in 4 days=7/60*4=7/15

Remaining work=1-7/15 = 8/15 [ (15*1-7)/15 = 8/15 ].

K.Nirdesh said: (Feb 1, 2012)
1/50+1/20) = (20+15)/300 //This get by cross multiplication. = 35/300 = 7/60. why we should Division do for (20+15)/300, how did the 300 is come?

Shro said: (Feb 16, 2012)
Thanku Prakash :).

Rinkesh said: (Feb 18, 2012)
Very simple, 15+20=35 15*20=300 35/300=7/60 work is 1 so=1-7/15 =15-7/15 Ans is = 8/15

Manoj said: (Mar 1, 2012)
Can you explain how did 7/60 come?

Manoj said: (Mar 1, 2012)
35/300=7/60 please explain it.

Thyag said: (Mar 11, 2012)
Hi Manoj, You need to simplify big number 35/300 in to small number for further calculation. So, you need to divide one common number of both numerator and denominator. You couldn't select 2, 3 and 4 as a dividing number. But you can use 5 as a common divider. If you divide 5 in both numerator and denominator, you will get 7/60. I hope your doubt clarified.

Anshu said: (Mar 31, 2012)
"A" can can do a work in 15 days therefore he did 1/15 of the work in a day. "B" can do the same work in 20 days therefore he did 1/20 of the work in a day. Therefore. [1/15 + 1/20]4 = [4/60 + 3/60]4. [7/60]4 = 7/15 of the work done. The total work left = 1 - 7/15 = 15 - 7/ 15 = 8/15.

Swamy Akunoori said: (Apr 1, 2012)
Good explanation anshu.

Esha said: (May 9, 2012)
How did 7/20 come?

Rashmi said: (May 16, 2012)
How did you get 7/60 please answer in simple method and tell how got 7.

Satish said: (Jun 6, 2012)
1/15+1/20= 7/60 How ? Please explain me clearly.

Pramesh said: (Jun 7, 2012)

@Rashmi, @Satish : 1/15 + 1/20 Now to make the denominator value equal take LCM i.e. , = (1*20) / (15*20) + (1*15) / (15*20) Now simplify these, i.e. , multiply the values i.e. , = (20/300) + (15/300). Now, both the denominator are equal, so you can add the numerator values i.e. , = (20+15) /300 = 35/300, Now simplifying this i.e. , cancelling both numerator and denominator by 5 (a common value which both will get cancel) ,

We get 7/60. Hope this will help you to understand the problem.

GUHAN said: (Jul 7, 2012)
@Swetha why mutiply with (A*TOTAL CAPACITY)?

Sanjana said: (Jul 28, 2012)
Thank you sundar nice explanation

Dipen said: (Aug 16, 2012)
How come Remaining work 1-7/15 (note:- why come 1 value )

Shiyamala said: (Aug 29, 2012)
A=1/15;B=1/20 [A+B]=[1/15+1/20] {1/1520/20=20/300; 1/2015/15=15/300} =20+15/1520 {cross multiplication} =35/300 {20+15=35;1520=300} =7/60 7/604=28/60 {47=28} =7/15

Ashish said: (Sep 24, 2012)
@Esha. It's not 7/20 its 7/60 and that came after addition of Both work A and B A+B= 1/15+1/20=20+15/15*20=35/300=7/60.

Mittal said: (Oct 1, 2012)
Plzz solve this A and B can together finish a work in 30 days. They worked at it for 20 days and then B let. The remaining work was done by A alone in 20 more days. B alone can do the entire work in. (a) 48 days (b) 50 days (c) 54 days (d) 60 days.

Sujit said: (Nov 16, 2012)

@Dipen: Probability is always .....Total chance = 1. If you say chances of wining a match is 1/2 i.e.(50%) it means chances of losing match is also 1/2 (50%)...how this losing chances 1/2 comes? It comes from subtracting wining chances from total chance that is : 1-1/2 = 1/2 Similarly in above question Remaining work = total work (1) - 4 day's work (7/15) = 8/15

Hope you get this...Have a great time :-)

Raj said: (Mar 16, 2013)
Can anyone explain answer for the below please? A and B can together do a piece of work in 30 days. B alone can do it in 40 days. A alone can do it in ? days. For me its coming 120 days. But in TNPSC ans is 140 days. please explain.

Arun D C said: (Jul 9, 2013)
@Raj, Here is the solution for yours. Given: A + B = 1/30 (A and B together can do the work in a single day). B = 1/40 (B alone can do the work in a single day). Solution: A = (A+B) - B. = 1/30 - 1/40. = (4-3) / 120. = 1 / 120. A = 1 / 120 (A alone can do the work in a single day). Therefore 'A' alone can complete the work in 120 days.

Carlo said: (Jul 26, 2013)
4(1/15 + 1/20) + X = 1. X = 8/15.

Kumar said: (Jul 28, 2013)
Why are we subtracting 7/15 from 1 ? Why not any other number?

Tinu said: (Aug 3, 2013)
Because a work is calculated as 1. If any value coming under fraction it comes between 0 to 1 so only. Like 15/15 = 1. Likewise Here we have 7/15 only, we need to know the remaining. 15/15-7/15 = 15-7/15 = 8/15.

DEEPAK said: (Sep 7, 2013)
A = 20, B = 15. TOTAL WORK FOR ONE DAYS = 7/60. 4 DAYS = 7/15. Remaining work = 8/15.

Mukesh Mishra said: (Sep 11, 2013)

A's 1 day work=1/15; B's 1 day work = 1/20. OK. Then we calculate how much A + B can do in 1 day. i.e. 1/15 + 1/20 ( in fraction if denominator is different first we find the l.c.m of denominator). So we calculate the l.c.m of 15 and 20 i.e 60(15 and 20 is divided by 5 we get the answer 3 and 4 so we find l.c.m by multiplying 5*3*4=60). 1/15*60+1/20*60 = 4+3/60 = 7/60. If A and B do work in 4 days = 7/60*4 = 7/15.

Remaining work = 1-7/15 = 8/15 [ (15*1-7)/15 = 8/15.

Geek said: (Sep 16, 2013)
1-((1/20+1/15)*4)==>1-7/15==>8/15. This is easy method, I think. If any other easy method please give me.

Sowmi said: (Sep 22, 2013)
Why the value of b had multiplied but in final there is a subtraction is held?

Kiran said: (Sep 28, 2013)
Can you explain How you got = (1/15+1/20) = 7/60?

Shiva said: (Oct 3, 2013)
@Kiran. (1/15+1/20) = (20+15)/300 //This get by cross multiplication. = 35/300. = 7/60. I think your doubt is clear now.

Viky said: (Oct 11, 2013)
I'm confused, can anybody tell me how 7/60 came?

Arpit Kashyap said: (Oct 13, 2013)
A's 1 day's work = 1/15, B's 1 day's work = 1/20, Since they work together for 4 days so that their left work in fraction = [1 - (1/15 + 1/20)]4. = (8/60)4. = 8/15.

Indu said: (Oct 19, 2013)
Short trick if you are use to of percentage: A's 1 day's work = 6.67% (100/15). B's 1 day's work = 5%. A+B's 1 day's work = 11.67%. A+B's 4 day's work = 46.68%. Remaining... 100-46.68 = 53.33% i.e. 8/15.

Vamshi said: (Oct 27, 2013)
@Deepa. (1/15+1/20) L.C.M of 15, 20 is 60. So 1/1560 = 4. And 1/2060 = 3. 4+3/60 = 7/60.

Ashik said: (Nov 15, 2013)
Why have you taken 1 as total work? HOW?

Jansi said: (Dec 24, 2013)
I understood upto 7/15. I can't understand how they are telling total work 1. From that they were minusing 7/15 can you explain me.

Gurdeep said: (Dec 30, 2013)
@Jansi. Both A and B doing the same (one) work, not different work.

Aravind said: (Jan 18, 2014)
We have to divide the denominator by its common divisible number and cross multiply it in numerator so you will get 7 then mutilply the highest remainder of lcm with the lowest denominator. You will get answer.

Thiyagu said: (Jan 29, 2014)
How the 0.53333 come 8/15 ?

Shrikant said: (Feb 11, 2014)
a/b + c/d. = ad/bd + cb/bd. = ad+cb/b*d. Maths rule if denominator not equal if equal directly cross multiplication.

Haphyz said: (Feb 26, 2014)

When dealing with addition or subtraction of fractions you consider the denominators i.e 15&20 and then you find the L.C.M which is 60 or multiply them together. 15*20 = 300 so, (1/15 + 1/20)/300 = (20 + 15)/300. =25/300 reduce to the lowest term and you get 7/60. This 7/60 is the amount of work A & B will complete in one day. Hence for 4 days we have; 7/60 * 4 = 7/15 of the total work. Since we don't know the real value of the total work we then assume total work to be done to be 1. Therefore, Remaining work left will be, 1- (work done) 1-7/15 ; the denominator here is 15 & 1 (since 1 =1/1). Do the math and you get our final answer to be 8/15. NOTE !

If you are subtracting a fraction from a whole number, just multiply the denominator by the whole number and then subtract from the numerator. The same rule applies for addition.

Shamanth Kumar Sm said: (Mar 10, 2014)
Can you explain how is 7/60 came?

Rajendra said: (Mar 11, 2014)
Good explanation but I can't understand how the 1- (7/15) is became 8/15.

Ellaiah Malli said: (Mar 15, 2014)

For 7/60. It is necessary to add both 1/15 and 1/20. But the denominators are different. So first we equals the denominators by multiplying with. Two different alternatives. i.e. 1/15*4/4. Because whenever we want to gave an alternative for multiplying. It should applicable to both numerator and denominator. That's why we use 4/4 for 1/15. As the same way for 1/20. We multiplying with 3. i.e. 1/20*3/3. Why I'm particularly take 4/4 and 3/3 particularly is. This is the minimum stage to equal both denominators, understand.

Now it is easy to add.

Nishi said: (May 16, 2014)
How did you get 7/15 after simplifying 7/60 ? Didn't understand the simplification of 7/60 to 7/15 Please explain.

Latha said: (May 20, 2014)
Work done=>4(1/15)+4(1/20) = 7/15. Remaining work = 1-7/15. = 8/15. Option D.

Mahesh Gehlot said: (Jul 6, 2014)
7/60 is the total work done by A and B in day 1. Therefore for 4 days we will calculate as below. 7/60 4 means when its multiplication we will divide. ie. 4/15 = 60 and we need to keep 7 integer as it was. Therefore we get 7/15. I don't know, Hope you'll understand this. A simple logic when its + or - we will cross multiply And when its we will divide. Thanks.

Prasad said: (Jul 11, 2014)
(1/15+1/20) = 7/60. Explanation: 15 = 53. 20 = 54. Here the common nums are 3,4,5. 345 = 60. 60/15 = 4. 60/20 = 3. (3/60+4/60) = 7/60.

Rajesh said: (Jul 12, 2014)
Why (1 - 7/15) ? What is total work as 1.

ANURAG SAXENA said: (Jul 20, 2014)
LCM - 15, 20. LCM = 60 UNIT. A-- 15 DAY -60/15 = 4 U/D B -- 20 DAY -60/20 = 3 U/D A+B = 7 U/D. 4 DAYS = 7x4 = 28 U. REAMING UNIT = 60-28 = 32 UNIT. REAMING WORK = 32/60 = 8/15 DAYS.

Prathyusha said: (Jul 22, 2014)
Why we takes total work as 1?

Prashant said: (Jul 22, 2014)
@Deepa. Actually when fraction occur. Then base must be same while doing it. 1/15 + 1/20 in this situation to calculate it base must be same. We can make it by multiply 1/15 By 4 and 1/20 By 3 so that it will be: 4/60 and 3/60 so.4/60 + 3/60 now we can do calculation result 7/60. I hope you understand what I mean to say?

Priya said: (Aug 2, 2014)
Is there any easy tricks to proceed further?

Krishna Gummani said: (Aug 12, 2014)
A can do a work in 15 days. B can do the work in 20 days. i.e. in one day the work completed by A and B is 1/15 and 1/20 respectively. In one day the work done by both A and B is, 1/15+1/20 = 7/60. If, for one day the work done is 7/60, then for four days? 7/604 = 28/60. The total work is 1. Work done in 4 days is 2860. Then, remaining work is to be done is 1-28/60. i.e. 8/15. Hence proved.

Kali said: (Aug 21, 2014)
1/15 = 4/60. 1/20 = 3/60. Simply add 4+3 = 7. And copy the denominator 60. LCD: 15 = 5x3. 20 = 5x4. LCD = 5x3x4 = 60.

Vikki Ls said: (Aug 25, 2014)
Hi sir, How would you calculate the 7/16*4 for to knowing the 4/15=60 ? Please tell me sir.

Deepak said: (Oct 7, 2014)
Why are using 1-7/15?

Srikanth said: (Oct 21, 2014)
In all these problems total work taken as "1" so we have to remove the resulting answer i.e., 7/15 from total work"1" so remaining work is (1-7/15) i.e., 8/15.

Sassy said: (Oct 27, 2014)
I'm not getting it at all can someone explain it why 70/60 in the easiest explanation please.

Rohit Wadile said: (Oct 29, 2014)
(ab)/a+b = work out. (1520)/15+20 = 4. 300/35 = 4. 7/15. Remaining Work = (1-7/15). Answer = 8/15.

Mounika said: (Oct 29, 2014)
Why 300 will come?

Sasi said: (Oct 30, 2014)

@Sassy. First, we have to calculate the work done for 1 day. For that we have to divide the number of days by 1. So, A's 1 day work = 1/15 and B's 1 day work = 1/20. Work done by A and B for 1 day is (1/15)+(1/20) = 7/60. Here, L.C.M is taken. As per question given, For 4 days, multiple with 4 then we can get. Work done by A and B for 4 days = 4(7/60) = 7/15. Here too L.C.M is taken. Total work is 1(Assumption). So,Work left = Total work - Work done by A and B. Therefore, work left = 1-(7/15) = 8/15. This is the answer.

I hope this helps you.

Mallarapusudhakar said: (Oct 31, 2014)
a = 15, b = 20, together c = 4 but LCM of in this 3 numbers is 60. So a is 15(4), b is 20(3) and c is 4(15). The first of 2 function is (4+3) remaining c(15). The total of LCM(60). 15-7 = 8. 8/60 answer.

Sunita said: (Nov 3, 2014)
Why they take like this 1-(7/15)?

Mangu said: (Nov 30, 2014)
Let's total total work is 1. A can do in 15 days. A can do it in 1 days = 1/15. Similarly B can do it = 1/20. They work totally in a day = 1/15+1/20 = 7/60. A and B do together in 4 days. So work done in 4 days = 7/60x4 = 7/15. Then left work is, Total work - 4 days work. i.e, 1-7/15 = 8/7 (Ans).

Karthikeyan said: (Dec 2, 2014)
Can you explain how 7/60 came? AND Next steps.

Rahul said: (Dec 3, 2014)
Can you just guide me to know that how can we calculate the LCM of says 8, 24, 60/7.

RDT said: (Dec 18, 2014)
@KARTHIKEYAN and @RAHUL. DONT CONFUSE. A can do in 15 days. A can do it in 1 days = 1/15. Similarly B can do it = 1/20. They work totally in a day. 1/15+1/20 = 35/300 = 7/60. Work done by A and B for 4 days = 4(7/60) = 7/15. So, Work left = Total work - Work done by A and B. Therefore, work left = 1-(7/15) = 8/15. This is the answer. I hope this helps you.

Shilambarasu said: (Dec 27, 2014)
I take LCM for a and b 15, 20 = 60. Now I take per day work a and b. a = 154 and b = 203. So both together work 60/7. Then I less 4 day work 4*7 = 28. So 60-28 = 32. Therefore 32/7 or 4.567. This is right or wrong please explain.

Prem said: (Dec 30, 2014)
7/60 = 20+15/300. But I am not understanding last step.

Ajay said: (Jan 2, 2015)
@Prem. Always remember that while solving percentage total is 100% and similarly in ratio the total is 1/1 i.e 1. Example : You can say that total work is done only when ratio comes in form of 1/1 , 2,2, 3,3,...... 50/50 and so on...... Answer will always come in 1/1(i.e total).

Sid said: (Jan 7, 2015)

LCM 15, 20 will give you 60 (the total work). LCM of 15 and 20, 5*3 = 15. 5*4 = 20. THEREFORE, 3*4*5 = 60. 1 day work of A = 60/15 = 4. 1 day work of B = 60/20 = 3. 1 day work of A and B together = 4 + 3 = 7 / 60. A and B worked together for 4 days = 4 * 7/60 = 28/60 = 7 / 15. Therefore, Work left = Total work - Work done in 4 days by A and B together. Work left (IN FRACTIONS) = 1 - 7/15 = (15-7)/15 = 8/15.

Thank you for giving me an opportunity.

L Raj Scope said: (Jan 14, 2015)
How to come [1/15+1/20] = 7/60?

Prasanth.sunny143 said: (Jan 16, 2015)

@L Raj Scope Please understand this concept first. LET CONSIDER A SIMPLE STATEMENT: A can do a work in 2 days. That means A's 1 day work = 1/2. This is the methodology we wanna apply on the data which is given in question. From the question. A (CAN D0 A JOB) ----15 days. B (CAN DO A JOB) ----20 days. Therefore by the above concept A's 1 day work = 1/15. B's 1 day work = 1/20. Therefore both A&B 1 work = (1/15)+1/20) = 7/60. NOW READ THE QUESTION. If A&B work together for 4 days then what the fraction of work left. Consider: Total work = 1. A&B (4 DAYS WORK) = (7/60)*4 = 7/15. REMAIN B WORK = (TOTAL WORK)-(COMPLETED WORK BY A&B FOR 4 DAYS). = 1-7/15. = 8/15.

Hope this is helpful.

Aravind said: (Jan 28, 2015)
Why calculate the remaining work (1-7/15) ? The question ask to find the fraction left.

Tricky said: (Feb 5, 2015)
Efficiency Method: Total 60 unit. A = 60/15 = 4. B = 60/20 = 3. Total = 7/60. In 4 days = 4*7/60 = 28/60 = 7/15. Remain = 1-7/15 = 8/15.

Vaibhav said: (Feb 23, 2015)
Why 1-7/15? The total no. of work is 1 do 1-7/15. If there are 2 works then 2-7/15. If 3 works then 3-7/15. And so on.

Sabaneak said: (Mar 10, 2015)
If remaining work is 8/15, how many days will it take A alone to complete the work.

Sweety said: (Mar 11, 2015)
A's 1 day's work = 1/15. B's 1 day's work = 1/20. (A + B) 's 1 day's work = (1+1) = 7. 15 20 60. (A + B) 's 4 day's work = (7x1) = 7. 60 4 15. Therefore, Remaining work = (1+7) = 8. 15 15.

Aravind_appu said: (Mar 17, 2015)
A = 1/15. B = 1/20. Together TH = A+B. TH = (1/15+1/20). TH/4 = (1/15+1/20). TH = 4((35/15*20)). TH = 7/15. = 1-7/15 = 8/15.

Anand said: (Apr 12, 2015)
Balance work = 8/15. A = 1/15, B = 1/20. Total no of days required to complete remaining work. A = (8/15) / (1/15) = 8 days, B = (8/15) / (1/20) = 10 2/3 days.

Merlin said: (Apr 21, 2015)
Can you just explain why they are subtracting the answer from 1?

Merlin said: (Apr 21, 2015)
Why do we make an assumption that the total work is 1?

Fuhar Choudhury said: (May 5, 2015)
I don't understand the logic behind solving such problems. Like people can assume anything anywhere I mean in the first problem itself you assumed let the amount of total work be one but why can't we take 2, 3, 4,..1001, etc. This is the reason mental maths eats me up mentally.

Mangesh said: (May 14, 2015)
When they not mention the quantity of work in problem in that case assume work done is 1. For e.g A can manufacture 1 chair in 15 days while B takes 20 days to manufacture 1 chair in this work done is only 1 that is to manufacture a chair but days require is different.

Akash said: (May 22, 2015)
Try to avoid fraction calculation. L.C.M of(15,20) = 60. Let total work is 60 unit. A can do 60/15 = 4 unit/day. B can do 60/20 = 3 unit/day. A+B can do = 4+3 = 7 unit/day. A+B in 4 day can do = 7*4 = 28 unit. Total work = 60 unit. Remaining work = 60-28 = 32 unit. Fraction of work = (Remaining work/Total work) = 32/60 = 8/15 (ans).

/mat said: (May 25, 2015)
Why 1/15, 1/20?

Devi Sri Prasad said: (Jun 8, 2015)
I think LCM is the best solution.

Avinash Ghadge said: (Jun 8, 2015)
@Deppa. 1/15 & 1/20 hear denominator are not same ok. So firstly we have to make both same. So 1/15 are multiply bye 4 on both numerator, denominator we get: 14/154 = 4/60. 13/203 = 3/60 this value are getting now adding this two value, we get. 4+3/60 = 7/60. That's it. I hope you understand.

PriyA said: (Jul 3, 2015)
But still I can't understand the logic behind the subtraction of 1. I have read @Mangesh answer. But why do we assume "one"? They did't mention anything right?

Priya said: (Jul 4, 2015)
Can any one please say, how (1-7/15) is applied?

Mounika said: (Jul 9, 2015)
'1' is the total work that has to be done. (It has to be taken by default in time and work). 7/15 is (A+B) 4 day's work. So, total work- (A+B) 's 4 day's work=work that is left to be done. 1-7/15 = 8/15.

Er.Ketan Patel said: (Jul 14, 2015)
Take LCM is 60 mean total work done is 60. It mean "a" can do 4 unit/day, "b" can do 3 unit/day. Total 3+4 = 7/60. Both do work together 4 days mean (7*4=28). They complete the work 28 (60-28=32). 32/60 = 8/15.

Sunil Jat Kantia said: (Jul 20, 2015)
Please solve this problem.

Nagasuriya said: (Aug 24, 2015)
Dear friends how to solve this calculate 7/60 x4 =7/15 please explain me?

Priya said: (Aug 31, 2015)
How 7 came please tell me again?

Naren said: (Sep 7, 2015)
Dear friends, I have the doubt that why we take the total work as 1 instead of taking 60. We take LCM of 15 & 20 as 60. So we consider 60 units as the total work. So we should take 60? Help me please.

Sushmoy said: (Sep 12, 2015)
(1-8/15) = 7/15 how is it possible? Please explain me.

Dnyaneshwar said: (Sep 15, 2015)
1*15 = 15. 15-8 = 7. So that denominator remains same 7/15.

Niral said: (Sep 16, 2015)
@Sushmoy. (1 - 7/15) = 8/15. Denominator of 1 will be 15 so it will be (15-7/15) = 8/15 will be answer.

Arafat Neloy said: (Oct 5, 2015)
A can do a work in 15 days and B in 20 days. A: 15 days-----1 work. 1 day-------1/15 work. 4 days------4/15 work. B: 20 days-----1 work. 1 day-------1/20 work. 4 days------4/20 work or 1/5 work. 4/15 + 1/5 = 7/15. Total work 1. So, remaining work (1-7/15). = 8/15 answer.

Mukesh Gautam said: (Oct 6, 2015)
Simple method: A-15. B-20. LCM is 60. 60/15 = 4. 60/20 = 3. Total work 60 an total unit work done by a and b is 7. In q4 day work are done than total 4 day work is 7x4 = 28. Remaining work 60-28 = 32. Fraction of remaining work is 32/60 = 8/15. Solution are done in only 20 sec. This method is very simple and less time consuming.

Priya said: (Oct 14, 2015)
Can you explain how this 7/15 came?

Birander Yadav said: (Oct 19, 2015)
1/15+1/20 = 7/60*2 = 7/15. Total work day = 1-7/15 = 8/15.

Shruti said: (Oct 23, 2015)
How 60 came?

Debasis Das said: (Oct 25, 2015)
A's 1 day work = 1/15. B's 1 day work = 1/20. Hence, A+B 1 day work = (1/15+1/20) = 7/60. So, A+B 4 day work = (7/60*4) = 7/15. Then, remaining work = 1-7/15 = 8/15.

ASHLYMOL SAJU said: (Oct 29, 2015)
A B A+B. 15 20 4. Work = Efficiency/Time. Work = LCM of A B A+B. W = 60. A B A+B = 4 3 15. Total = 7/15. Remaining = 8/15.

Jinto said: (Nov 4, 2015)
(A+B) 's 1 day's work = 7/60. So (A+B) can finish the work in 60/7 day. (A+B) 's 4 day's work = 7/15. So remaining work = (60/7) - (7/15). Is this correct? Why remaining work = (1-7/15), from where 1 came?

LOURDHU RANI said: (Nov 12, 2015)
How came 1-7/15 step, I don't understand?

BIKASH SAHOO said: (Nov 23, 2015)
(1-7/15) this process I can not understood.

Ashwini said: (Dec 12, 2015)
Its very simple 1/1-7/15. LCM between 1 and 15 is 15. So = (1/1)(15/15) - (7/15)(1/1) {Make both the denominator as 15 i.e LCM}. = 15/15 - 7/15. = (15-7)/15 = 8/15. Hope understood!

Dinesh said: (Dec 16, 2015)
This problem ok I can understand but some other problems I can't understand my dear friends.

RANGADHAR said: (Dec 24, 2015)
If the total work is taking the LCM of 15 & 20. Then it will be 60. A = 15 days. B = 20 days. LCM = 60 work. Then A do in one day = 60/15 = 4 work. B = 60/20 = 3 work. In one day they work = {4+3} work. In 4 days = 7*4 = 28 works. Remaining = 60-28 = 32 work. Then 32/60 = 8/15.

Bhargav said: (Dec 25, 2015)
I don't understand why we take 1-7/15?

Mohsin said: (Dec 26, 2015)
How (7/60*4) = 7/15?

Sumit Sharma said: (Jan 4, 2016)
Please some one tell how 1/10:1/15:1/20 comes 6:4:3?

Mitsuna said: (Jan 5, 2016)
"From the above answer, we can say 15/8 days required to. Complete the remaining work by A and B". Can you please calculate this in whole number so that we can assume the exact days remaining?

Sudhansu said: (Feb 3, 2016)
1-7/15 applied because the whole work is 1.

RPV said: (Feb 9, 2016)
Why in this sum answer is not reciprocated in time and work problem the answer must be in reciprocal? Ex. 8/15 is written as 15/8 am correct.

RPV said: (Feb 9, 2016)
Tulsi and Ram can do a job alone in 20 days and 30 days respectively. In how many days the job will be finished if they work together?

Shashi Kant said: (Feb 11, 2016)
A's days = 15. B's days = 20. LCM of both = 60 (total work also). A's work per day = 60/15 = 4. B's work per day = 60/20 = 3. Both can do work in one day = (4+3) = 7. 4 days work of both = 7*4 = 28. Then remaining work = (60-28) = 32. So please tell me how can I fractionate it?

Keshav said: (Feb 16, 2016)
Nice explanation.

Mouni said: (Feb 17, 2016)
A's days = 15. B's days = 20. LCM of both = 60 (total work also). A's work per day = 60/15 = 4. B's work per day = 60/20 = 3. Both can do work in one day = (4+3) = 7. 4 days work of both = 7*4 = 28. Then remaining work = (60-28) = 32. So please tell me how can I fractionate it?

ANI KONAR said: (Feb 22, 2016)
Short trick: 15, 20 LCM 60. 4, 3 efficiency. 4 + 3 = 7 in 1 day. 7 * 4 = 28 in 4 days. Remaining = 60 - 28 = 32. In fraction 32/60 = 8/15.

Harkanwal said: (Mar 10, 2016)
Why 32 by 60? Explain in detail.

Basivireddy said: (Mar 11, 2016)
Hi guys, this is Basivireddy. A can be work in 15 days = 1/15. B Can be work in 30 days = 1/30. 1/15 + 1/30. 7/60 this is one day work. We want 4 days work that's why it is 4*7/60 = 28/60 = 7/15. Now one day work means they left one day so. 1-7/15 = 8/15, I hope so you understood, Thank you guys, have a great day.

Vikas said: (Mar 16, 2016)
Can you explain how is 7/60 came?

GANESH said: (Mar 25, 2016)
A do the work in 1 day is = 1/15. B do the work in 1 day is = 1/20. So LCM of 15, 20 is = 60. Now, A's work is 1/15 * 60 = 4. B's work is 1/20 * 60 = 3. Then (4 + 3/60) = 7/60. 7/60 is one day work of A+B. We want 4 days work of A+B. Then, (4 * 7/60) = 28/60. => 7/15. Now one day work is (1 - 7/15) = 15 - 7/15. => 8/15 is the answer.

Nanda said: (Mar 29, 2016)
How you got 7/15?

Anoof said: (Mar 31, 2016)
60 divides 4 by 15 times that means 4 * 15 = 60.

Sushant said: (Apr 4, 2016)
How 7/60 come? How to solve 1/15 + 1/20? Explain me.

Ashwini G C said: (Apr 16, 2016)
Hi friends, Happy to see you all discussing the problems and the solution given by each of them is awesome. In fact, I could solve the problem by seeing this 'discussion forum'. I had all the doubts as others had and I used to get a solution for it. So, I thought of thanking you all.

Rasim Shaikh said: (Apr 22, 2016)
Hello, friends! Can anybody tell, how 1-7/15 get a plus? and I can't understand where the 1 come? Please help me.

Deepa said: (Apr 26, 2016)
@Swetha. Thanks! Your explanation is very good and it is easy to understand.

Harry said: (May 18, 2016)
I just came across an extremely easy way of solving this question. So felt like sharing it. Work = LCM (15, 20) = 60 units. A does 60/15 i.e. 4 units in a day, B does 60/20 i.e. 3 units in a day. In 4 days work completed = (4 + 3) * 4 = 28 units. Work left = Total work - work done by AB = 60 - 28 = 32 So, Fraction of Work left = 32/60 = 8/15.

Deepa said: (Jun 27, 2016)
I'm confused with this stem (1 - 7/15). Can anyone explain this?

Arun said: (Jul 10, 2016)
Harry is correct. Hi @Deepa, leave that 1-7/15 & %method, simply total efficiency is 7/day, no of worked together is 4, then multiply it becomes 28. Subtract from total work done 60 - 28 = 32. To find the answer for ques-> 32/60 = 8/15. Cool.

Krishna said: (Jul 22, 2016)
I'm confused with this step (1 - 7/15). Can anyone explain this?

Pradosh Behera said: (Jul 27, 2016)
Work is 1part. A and B work is finished 7/15 part in 4days from 1part. Remaining work is 1 - 7/15 = 8/15.

Meena said: (Jul 31, 2016)
Fraction of work done in 4 days = 7/15. (It means that out of 15 parts, 7 parts has been done. So 8 parts left) Therefore, the fraction of work left = 8/15.

Santanu said: (Aug 2, 2016)

For those who have difficulty with fractions, here is an alternative. Let the total work be to lay 120 bricks. (I chose 120 as it can be divided easily by both 15 and 20). Takes 15 days to lay 120 bricks, That means in one day he can lay 8 bricks. B takes 20 days to lay 120 bricks. That means B can lay only 6 bricks in one day. Together they can lay 8+6=14 bricks. Therefore, in 4 days, they will lay 14*4= 56 bricks only. Remaining bricks to be layed is 120-56=64 bricks.

That means, 64/120=8/15 of the work is remaining.

MUHAMMAD SHAHID ZAFAR said: (Aug 3, 2016)
Why you subtract 7/15 from 1?

Sammed said: (Aug 17, 2016)
Thank you, everyone those have written explanation here. It really helps.

Raju said: (Sep 14, 2016)
In how many days A & B together complete the same job?

Joni said: (Sep 16, 2016)
Elaborate how you do this (1/50+1/20) where did you get 1/50?

Argan Defar said: (Sep 22, 2016)
For the Question of @Raju, (A + B)'s completion days = (A * B/(A + B)), => 15 * 20/(20 + 15), => 300/35 = 8.6 days.

Pratik D. said: (Sep 28, 2016)

Since our target is to crack for the competitive exam which means we must do problems as fast as we can to save time, in other words in a short cut way. Now, for this question, lets suppose they are making chairs (the work). A takes 15 days. B takes 20 days. Then LCM of 15, 20 is 60. Capacity of A = 4 chair/day and capacity of B = 3 chairs/day. So A + B capacity in one day = 4 + 3 = 7 chairs/day, The question says for 4 days they worked together. ie (7 * 4 = 28). Remaining = 60 - 28 = 32.

Fraction of work remaining = 32/60 = 8/15.

Dipu Ahmed said: (Oct 7, 2016)
Here, A works 1/15 in 1 day. B works 1/20 in 1 day. So, A + B works (1/15 + 1/20) = 7/60 in 1 day. So, if A + B works together 7/60 in 1 day. Then A + B works together (7/60 * 4) = 8/15 in 4 day. If we assume that 1 is the full work and A+B works together 8/15 in 4 days . The remaining works we get by {full work - (A + B)'s 4 days completed works}. So , (1 - 8/15) = 7/15. So, the answer is 7/15.

Asshok said: (Oct 29, 2016)
Why 1 - 7/15? Explain it.

Kennethy said: (Nov 4, 2016)
@ Vishwanath. 7/60 * 4 = 7/15. This is how; It's like multiplying 7/60 by 4/1 = 7 * 4/60 * 1 This gives us 28/60. We get a common divisor of the numerator and denominator which is 4. Hence it is 7/15.

Sri said: (Nov 11, 2016)
Please give the short trick 'with efficiency' then the sum will be solved very quickly.

Mani said: (Nov 24, 2016)
How to find the solution of this question? Please solve this by easy method.

Israel said: (Nov 27, 2016)

A can do the work in 15days, hence he does 1/15 of the work in a day. B can do the work in 20days, hence he does 1/20 of the work in a day. Working together, they will do (1/15)+(1/20)= 7/60 of the total work. In 4 days, they would have done 4 * (7/60) = 7/15 of the total work (E.g they have built 7 houses out of the 15 houses they were to build). Hence, they need to build 8 more houses to complete their work. That is how we get 8/15 as the FRACTION of work remaining.

I hope that was comprehensive enough.

Koteswararao Chimmili said: (Dec 6, 2016)
A's 1 day's work = 1/15; B's 1 day's work = 1/20; (A + B)'s 1 day's work = (1/15 + 1/20) LCM = 60 5 \| 15 , 20 __________ 3 , 4 = 534 = 60 (A + B)'s 1 day's work = (4/60 + 3/60) ( 4/60 = 1/15 AND 3/60 =1/20 ) = 7/60 (A + B)'s 4 day's work = 7/60*4 = 28/60 = 7/15 . Therefore, Remaining work = (1 - 7/15) = (15-7)/15 = 8/15.

Vikrant said: (Dec 7, 2016)
Simple that how get 7/60. 15 + 20/15 * 20 = 35 / 300. So, 7 * 5 = 35 & 60 * 5 = 300. Thats it!

Innareddy Chilakala said: (Jan 3, 2017)
(15 * 20)/15 + 20 = 60/7. Work done in 4 days (7/60) * 4 = 7/15, Remaining work is 1 - 7/15 = 8/15.

Vivek said: (Jan 7, 2017)
How 7/60 came?

Ramkali said: (Feb 3, 2017)
Why do we want to calculate 1-7/15?

Sunita Devi said: (Feb 18, 2017)
Why this answer is not sufficient at this term : (7/15)? Why do this term (1-8/15)?

Ammu said: (Apr 1, 2017)
A's 1 day work = 1/15. B's 1 day work = 1/20. Together for 1 day=(1/15+1/20), =(4+3)/60, =7/60. together for 4 days=(7/60) * 4, = 7/15. If total work is 1. Then the rest is = 1 - 7/15, = 8/15.

Santhosh said: (Apr 6, 2017)
Can anyone explain this in LCM method?

Prashant Devada said: (Apr 10, 2017)
@Akash. You are great, LCM concept makes easy to understand. Thanks.

Praveen Behera said: (Apr 12, 2017)
Why (1- 7/15) is applied as 8/15? Can anybody explain it please?

Juhi Saxena said: (Apr 26, 2017)
If both 1 day work is 7 then 4 days work is 28 and remaining is 32 how can I change it into fraction? Please explain.

Dhanalakshmi said: (May 5, 2017)
Thanks for your explanation @Swetha.

Shubham said: (May 14, 2017)
Thanks for the explanation @Swetha.

SUNDARA said: (Jun 3, 2017)
A & B together requires 1/15+1/20=7/60 or 60/7days =8 4/7 days to complete the work. After 4 days work, pending work is 8 4/7 -4=4 4/7days work. = 4 4/7 divide by 8 4/7=32/7 divide 60/7=32/60=8/15 work pending.

Pooja said: (Jun 11, 2017)
How, (7/60 * 4) = 7/15?

Aadesh said: (Jul 6, 2017)
28/60=14/30=7/15 @Pooja.

San said: (Jul 12, 2017)
Here, 1/15+1/20= 20+15/300= 35/300 =7/60.

Karthik said: (Jul 18, 2017)
how 1-7/15 came? Please explain it clearly.

Yona said: (Jul 18, 2017)
According to me, =(4/15+4/20), =(140/300), =(7/15).

Rahul Manjhi said: (Aug 6, 2017)
If A can do work in 15days then in 4days will be=4/15, Similarly, if B can do work in 20days then 4days will be=4/20=1/5, Therefore adding A and b together=4/15+1/5=7/15, Now remaining work=1-7/15=8/15.

Ankit Kain said: (Aug 19, 2017)
Here is the perfect solution. L.C.M- 60 (it is the lcm of 15 and 20 and here it is total work) A's---------15 days\|---EFFICIENCY-60÷15=4 (because, work= efficiency * time) B's---------20 days\|---EFFICIENCY-60÷20=3 combined efficiency of A and B =7. work done by (A+B) in 4 days= 7 * 4=28(because work = efficiency * time). hence ratio---------> 28/60=8/15.

Sagar said: (Sep 5, 2017)
How to 300 come? Explain.

Shubham Mishra said: (Sep 7, 2017)
@Ankit kain. In the last step why you take 28/60 instead of 60/28?

NISHA said: (Sep 8, 2017)
Why sub this (1-7/15) can you explain?

Jenifer said: (Sep 11, 2017)
@Shubam Mishra. Because 60 is just the value of L.C.M.

Shiva said: (Sep 20, 2017)
Why sub (1-7/15)? please explain.

Asi Ganesh said: (Sep 23, 2017)
Why sub (1-7/15)? I can explain 7/15 is A, B are together work in 4 days Then question is remaining work is nothing but left this work is total work is 1 and remaining work is is nothing but all of you know (1-7/15)=8/15.

Karthik said: (Nov 16, 2017)
How comes 300 please explain?

Prabhu said: (Dec 6, 2017)
Can anyone solve this? Problem: 'A' can do a piece of in 6days, 'B' in 9days and 'C' in 12 days. In how many days will all of the together finish the work?

Dhananjay Moundekar said: (Dec 12, 2017)
@Prabhu. 6d/w <= A---->6d 4d/w <= B---->9d 3d/w <= C----->12d Total Work is LCM of A,B,C =36W They All do toghether means, A+B+C=>6+4+3=13d/w Therefore, A + B + C = 36w/13d/w=2*10/13.

Sneha said: (Dec 19, 2017)
Therefore, A + B + C = 36w/13d/w=2*10/13. How is it? please explain.

Atma Kumar Vishwakarma said: (Dec 29, 2017)

Let both making toffee. The total toffee they made is 60 it LCM of 20 and15. mins A make 60 toffee in 15 days it mins A make 4 toffee a day, B makes 60 toffee in 20 days it mins B make 3 toffy a day they work together for day it mins (3+4)*4=28. In 4 days they made 28 toffee they need to make 60 toffee.

It mins 28/60=7/15.

Pooja said: (Feb 6, 2018)
Why we subtract 7/15 by 1?

Komal said: (Feb 20, 2018)
Can you explain how 7/60 came?

Ashik said: (Mar 4, 2018)
If we calculate A and B 's work together 1/15+1/20 then it will came?

Anu said: (Mar 14, 2018)
How come 7/60?

Miru said: (Mar 20, 2018)
1-{4(1/15+1/20)} =1-{4*7/60} =1-1/15 8/15 is the answer (d).

Mogarg said: (Mar 28, 2018)
@All Here is the Concept of 1. If a can do work in 5 days, then, In one day = 1/5. In 5 days = 1/5+1/5+1/5+1/5+1/5. = 5/5 =1. the concept of 1 means total work, not a day so assume our total work 1.

Abhinesh said: (May 25, 2018)
Let, Do in this way; Use formula= xy/x+y. X is 15 and Y 30 if you cross multiply you get an answer.

TRUPTIMAYEE BAHINIPATI said: (May 26, 2018)
Why we subtract 7/15 by 1? Solution: Here we consider that the total work is 1. A&B do a certain work that we don't know so at first we need find the unit of work in 1day then A+B's working unit per 4 days. After that we got A&B's total unit of work done ;which is substrated by 1 to got the remaining work.

Fazeena said: (May 30, 2018)
I can't understand 1-7/15. So, please explain me again or another way.

Jagannath Naik said: (Jun 4, 2018)
How to find 1/15?

Nikhil said: (Jun 6, 2018)
@Fazeena. The work completed in 4 days is 7/15. Therefore remaining work is 1-(7/15). So, total work is 1.

Krish Magesh said: (Jun 9, 2018)
A's 1 day's work = 1/15. B's 1 day's work = 1/20. (A+B)'s 1 day's work= (1/15+1/20), = 20+15/300(cross multiplication), = 35/300, = 7/60. (A+B)'s 4 day's work= 7/60 * 4, = 7/15(60/4 is division it is 15). Therefore remaining work=1 - 7/15, = 15-7/15, = 8/15.

Leela Krishna said: (Jun 17, 2018)
Can you explain the step 7÷60?

Laxman said: (Jul 10, 2018)
A's 1 day's work = 1/15. B's 1 day's work = 1/20. (A+B)'s 1 day's work= (1/15+1/20), L.C.M of 15,20 is 60 then, 154=60, 203=60, 4 + 3/60=7/60.

Sasikumar said: (Jul 12, 2018)
The total work of A& B is = 60. we can get 60 by taking LCM of it. A's one day work = 4. B's one day work = 3. Both A & B 's one day work=7. A's 4days work=44=16. B's 4 days work=43=12. So, A&B work=28. The remaining work=60-28=32. = 32/60, = 8/15.

Vinay Gudipati said: (Jul 25, 2018)
Very simple, 15+20=35, 15*20=300, 35/300=7/60, work is 1 so=1-7/15. =15-7/15, Ans is = 8/15.

Tabbu said: (Jul 25, 2018)
Please explain this step 1-7/15.

Priya said: (Aug 21, 2018)
A can do work in 15 days=1/15. B can do work in 20 days=1/20. both (A+B)=1/15+1/20=20+15/300=35/300=7/60. (A+B)Work together in 4 days=7/60*4 in this 60 will be cancelled 4 table in 15. Then; times=>7/15. The remaining work will be(1-7/15). =>15-7/15. =>8/15.

Raghavan said: (Sep 16, 2018)
The LCM of 15 and 20 is 60 which means total work done=60. Then the efficiency of a & b are 4 & 3 respectively(one-day efficiency). Now if both work together their efficiencies must be added which is =7 and therefore 7*4=24. Is the work was done by them for 4 days which means the leftover is 60-24=36. Am I right?

Shurti said: (Nov 3, 2018)
@Tabbu. Here 1 means the whole part. So subtract the work done from the whole work to get remaining work.

Sai Kumar Reddy said: (Dec 9, 2018)
The common Multiple for 15 and 20 is 5. A's one day work =155=75 units, B's one day work =20/5=4 units, Both working together for 4 days=74=28 units.

Esha said: (Jan 22, 2019)
We consider work done in 15days=1/15 that means a piece of work done in 15 days. Similarly work done in 20 days = 1/20. So the question is asked for 4 days which means 1/4. So we consider the remaining work to be done as 1.

Subho said: (Jan 30, 2019)
Kindly solve it in ratio method.

Raj said: (Mar 1, 2019)
How 1-(7/15)=8/15? Please explain.

Manikkam said: (Apr 16, 2019)
1- (7/5) = 8/5. Because we consider the whole work as 1 then A and B together complete their job for 4 days is 7/5. Then in the question, they are asking that the fraction of the remaining work so we subtract those values.

Meenu said: (Jun 9, 2019)
Thanks for explaining @Swetha.

Vikaah Yadav said: (Jul 17, 2019)
Thank for the explanation @Vikash.

Pooja said: (Jul 20, 2019)
How 7/60 came? Please explain me to get it.

Divye said: (Aug 5, 2019)

A can complete work in 15 days. B can complete work in 20 days. total work (in units) = L.C.M of 15 and 20 => 60 units. Unit work of A = Total work (in units)/Number of days A take to complete work => 60/15 = 4. Unit work of B = Total work (in units)/Number of days B take to complete work => 60/20 = 3. Work done in 1 day by A and B together = Unit work done by A + Unit work done by B => 4+3 = 7. Work done by A and B together in 4 days = Work done by A and B together in 1 day * 4 => 7 * 4=28.

Work left = Total unit of work - work done by A and B together in 4 days => 60 - 28 = 32.

Rushikesh said: (Aug 19, 2019)
@Pooja (1/15)+(1/20). [(20+15)/(15*20)], = 35/300, = 7/60.

Swetha said: (Oct 18, 2019)
We know A done his work in 15 days and B in 20 days so total work is we take as 1.work is inversely proportion to days 1÷15 +1÷20=(15+20)/15x20=35/300=7/60=7x4/60=28/60=1-28/60=8/15. Here 1 indicates total work.

Chandradeepa said: (Dec 25, 2019)
By considering LCM 60 in that case why should we need to do remaining work divided by total work.

Sufiyan said: (Jan 10, 2020)
A' work is (1÷15) in one day, B's work is (1÷20) in one day, If both perform the work together then (1÷15)+(1÷20)=(35÷300) work is done in one day. Now multiplying it by 4 so we get the amount of work done in 4 days. (35÷300)*4 = (7÷15). Now we know the total amount of work is 1. Then subtract (1)-(7÷15)=(8÷15) the remaining work.

Timilsina said: (Jan 10, 2020)
A=1/15 and b=1/20 ,a+b=7/60*4 =7/15 so, 1-7/15 = 8/15.

Harsh said: (Feb 27, 2020)
Can you explain why you have put 1_7/15?

Virat said: (Mar 15, 2020)
A=15 Days. B=20 Days. LCM 60. A's 1 Day work=4. B's 1 Day work=3. Both together 1 Day work= 7/60. Both together 4 Days work= 28/60. Rest work= 32/60 = 8/15.

Billal Hossin said: (Jul 13, 2020)
@All. According to me, it can be solve by 2 methods. Method- 1: A's 1 day work = 1/15. B's 1 day work= 1/40. (A+B)'s 1 day work= (1/15)+(1/40). = (8+6) /120. = 14/120. = 7/60, (A+B)'s 4 days work= (7*4)/600, = 7/15, Left work is= 1- (7/15 ), = 8/15 (Ans). Method-2: (A+B)'s 4 days work= (4/15)+(4/20), = (4/15)+(1/5), = 7/15. Left work= 1- (7/15). = 8/15 (Ans).

Vishnu said: (Sep 23, 2020)
Good, thanks @Billal Hossin.

Kundan said: (Oct 22, 2020)
A one day work = 1/15. B one day work = 1/20. One day work of both = 1/15 + 1/20 = 7/60. 4days work of both = 7/60 * 4 = 7/15 is the total work of 4days. So, remaining days work = 1 - 7/15 = 8/15. Hence, 8/15 answer.

Yeswanth said: (Nov 8, 2020)
A's 1 day's work =1/15. B's 1 day's work =1/20. (A + B)'s 1 day's work = (1/15 + 1/20) = 7/60. (A + B)'s 4 day's work = 4 * (7/60) = 28/60. In 4 days they complete 28 parts of work out of 60 parts of work. Rest of work is 32 parts. :=> 32/60 has to be completed i.e 8/15.

Surya said: (Jan 20, 2021)
(1/15+1/20). Fractions of 15 and 20 are written as; 35 and 2'2 5. = 60, and 35 go for 7, = 7/60.

Lohith said: (Jan 29, 2021)
How (1/15+1/20 )= 7/60? Explain, please.

SR Ranees said: (Feb 12, 2021)
Explination for (1/15 + 1/20) = 7/60, take LCM of 15 and 20. LCM will be 60, = (14/154) + (13/203), = (4+3)/60, = 7/60.

MEGA MATH said: (Mar 4, 2021)
1/15 + 1/20 = 7/60, 7/60*4 = 28/60, If we simplify 28/60 by 4, then it is 8/15.

Asha Shetty said: (Mar 12, 2021)
@Mega math. I can't understand how t simplify 28/60 by 4 and how it becomes 8/15?

Palak said: (Apr 8, 2021)
Thanks all.

Joel said: (May 14, 2021)
Lets take total work is = 1. In 15 days A will complete the work; In one day he comlete 1/15 part of work, Similarly B comletes 1/20 work in one day. Hence A and B both completes 1/15 + 1/20 work in one day 1/15+1/20 = 7/60. A and B's one day work, thier 4 days work = 4 * (7/60) = 28/60 = >7/15, Now total work is 1, They completed 7/15 work in 4 days, Now remaining work is1-7/15 = 8/15.

Ashutosh Sharma said: (Jul 21, 2021)
A takes 15 days & B takes 20 days. L.C.M. of 15 and 20 is 60 ( Total work) Then A works in a day 60÷15 = 4 &, B works in a day 60÷20 = 3. When both works together; A+B works in a day (4+3) = 7. They works for 4 days then 7*4 = 28, Remaining work is 60 - 28 = 32, The fraction of left work is 32/60 = 8/15.

Jigme Wangchuk said: (Aug 5, 2021)
Simple method. A = 15 days, B = 20 days, No days of work together (A+B) = 4 days, Fraction of work = 4* sum/product. = 4(15+20/1520) =140/300 simplify = 7/15. Now, remaining fraction of work = 1-7/15 = 8/15.

SkiGi said: (Oct 6, 2021)
Why 7/60? I don't understand, please someone explain.

Yusuf said: (Nov 19, 2021)
A+b 1 days work =7/60.

Abishek Thapa said: (Nov 28, 2021)

LCM of A's and B's: A-15 B-20. LCM is 60 (It is also total Work) and Efficiency is TOTAL WORK/ TIME i.e. 60/15 = 4 <<<A's 1 day Efficiency 60/20 = 3 <<<B's 1 day Efficiency. Combining both 1-day Efficiency then we get 4+3=7 (It means A and B can do 7 units in 1 day) According to the question: if they have 7 unit Efficiency they work for 4 days then we get: 7 x 4 and divide by total work (60). 7 x 4/60= 7/15 << it is the part of work they will finish in 4 days. But the question was asked about how much fraction is left then simply we know that total work is 1 then subtract total work 1-7/15.

We get 8/15 that is the answer.

Md Afif said: (Jan 16, 2022)
How 1-7/15? Explain.

Jyothi said: (Feb 3, 2022)
I am not getting. How 1-7/15? Explain, please.

Ankita said: (Feb 12, 2022)
@Jyoti. It's 1 -7/15 as it is asking how much work is left. Which means 1 is the total amount of work, and 7/15 is the amount of work completed. So, to get the remaining work we hv to subtract the work done by the whole work. Which is 1-7/15. = 15/15 - 7/15. = 15-7/15. = 8/15. Hope it helps.

AKT said: (Mar 23, 2022)
Thanks everyone for explaining the answer.

Swetha said: (Mar 28, 2022)
First of all, thank you to explain the method. I have a doubt that how we know to take (i.e Total work = 60)? Anyone, please help me to get it.

VisHnu RaM said: (Apr 7, 2022)
Thank you for giving the clear explanation @Swetha. And 60 will come, No of days LCM 15 days to 15 * 4 = 60. 20 days to 20 * 3 = 60. So, the LCM is 60.

Dibyanshu said: (Aug 5, 2022)
A - 15 days. B - 20 days. LCM of 15 & 20 is 60 (The total work is 60 also). So, The Efficiency of one day's work is 60/15 = 4 and 60/20 = 3. Then, both A & B can complete the work in one day is 4+3=7. They worked for 4 days, so 7x4=28 Work completed in 4days by both A+B=28. Then, rest work = Total work - Completed work Rest work = 60-28=32. 32/60 = 8/15 The answer is = 8/15.