Is twice as fast as B and is therefore able to finish a work in 30 days less than B find the time in which they can do it working together?

24.

A works twice as fast as B. If B can complete a work in 12 days independently, the number of days in which A and B can together finish the work in :

Answer: Option A

Explanation:

Ratio of rates of working of A and B = 2 : 1.

So, ratio of times taken = 1 : 2.

B's 1 day's work =	1	.
12

A's 1 day's work =	1	; (2 times of B's work)
6

(A + B)'s 1 day's work =		1	+	1		=	3	=	1	.
6	12	12	4

So, A and B together can finish the work in 4 days.

Paandu said: (Jan 26, 2011)
Why we are ratio this problem and ratio of times taken = 1:2 ?

Ghousia said: (Mar 5, 2011)
simplest method: A is twice of B then B=2A B completes work in=12 then 2A=12=>A=6 A's 1 day work=1/6, B's 1 day work=1/12 (A+B)'s 1 day work=(1/6+1/12)=3/12=1/4 now (A+B) together finish work in 4days

Arun Pandian said: (Jul 8, 2011)
SHORT CUT METHOD: let x=2(bcz A is twice as fast as B) n=12(bcz B completes the work in 12 days) use the formula:A&B together do the work in p days as follows p=n/x+1 =12/3 =4days

Umeshprasad said: (Nov 19, 2011)
Let A's 1 day work is x B's 1 day work is 1/12 from question a is twice as fast as B so A=2B------------(1) x=2*1/12=>1/6 which is one day work of A combine one day work of A and B is (1/6)+(1/12) which will give u 1/4 so the entire work they will finish in 4 day.

Deepa said: (Feb 17, 2012)
B'S one day work=1/12 A'S one day work=2(1/12)=1/6 (A+B) one day work=(1/12)+(1/6)=1/4 hence A and B together complete the work in 4 days

Kapil said: (Feb 20, 2012)
Simple : A 's twice ie Half of B. . .So B is 1/12 thn Frm tis A is 1/12. . .thn A+B we get t Ans. . .

Omkar said: (Sep 27, 2013)
A = 2B. Hence, A+B = 2B + B i.e. as good as three Bs working together. B completes in 12 Days, 3B will take 1/3rd of the time i.e. 12/3 = 4.

Atul1487 said: (Apr 29, 2014)
Simple method without any rubbish ratio. Suppose B completes 1 work in x days. So B completed work in 1 day = 1/x.............1. Now A completes 1 work = x/2 (Cz A is twice faster than B). So A completed work in 1 day = 2/x.............2. Together their Work = 1/x + 2 /x. Given x = 12. So, Together their Work = 1/12 + 2 /12. == 1/12 + 1/6. ==1/4 or 4 days. No ratio - nothing complicated.

Swati said: (Oct 1, 2014)
SHORTCUT: A is twice efficient as B that means If B takes 12 days then A will take 6 days. Now both are working together. So definitely together they'll take less than 6 days. ONLY option less than 6 days is Option A i.e. 4 days.

Aravind_appu said: (Mar 17, 2015)
A = 2b------(1). B = 1/12------(2). 1 sub in 2. A = 2(1/12). A = 1/6. Total work is done TH = A+B. TH = (1/6+1/12). = (12+6)/(6*12). = (18/72). = 1/4. = 4 day exactly.

Deepa said: (May 30, 2015)
A:B = 1:2. B can complete a work in 12 days. Let A can complete in X days. X:12 = 1:2. X = 1*12/2. X = 6 i.e, A = 6. (A+B) 1 day work = 1/6+1/12 = 1/4. So, A and B finish work in 4 days.

Inna Reddy Chilakala said: (Feb 9, 2016)
A : B = 2 : 1 (work). B = 12. A can finish work 1 --- 12. 2 ---- 6. A+B = 12*6/12+6 = 4.

Kashish said: (Jun 21, 2016)
More easy solution Guys. Let assume that B take X time, so A will take 2X. So now there 1 Days work will 1/x + 2/x = 3/x. Now from question, they work for 12 days, 3/x = 12. x = 3/12. x = 4 ->Answer.

Sudhanshu said: (Dec 25, 2016)
T --------- W B --------- 1 1/12 A ---------1 1/6 If A+B work W --------- T( days) 1/4 --------- 1/1/4. It comes 4days.

Sudhanshu said: (Dec 25, 2016)
T --------- W B --------- 1 1/12 A ---------1 1/6 If A+B work W --------- T( days) 1/4 --------- 1/1/4. It comes 4days.

Vaishnavi Kokate said: (Feb 2, 2017)
Let, A = 20 B = 10 because A works twice as fast as B. Total work, B = 10 * 12=120 because B completes his work in 12 days. so A + B/total work. 120/30 = 4 days.

Arnab said: (May 13, 2017)
A works twice as fast as B means, The efficiency of A : B = 2:1 (efficiency means per day work), A does in 1 day 2 units work. B does in 1 day 1 unit work. (A+B) together do in 1 day = 3 units work. Total work = 1* 12 = 12 units (as per question B can complete a work in 12 days). (A+B) can do together = 12/ 3 days = 4 days. (Ans.)

Amrit said: (Jul 18, 2018)
suppose B =x; and A works twice =2x, then the total amount of work is; 2x+x=12; 3x=12, x = 4.

Rajat Pundir said: (Sep 17, 2018)
a/b=2/1. Now using the ratio method. 1/12=1/3*(a+b). 1/4=a+b. Hence 4 days.

Ashish said: (Nov 1, 2018)
what is 1:2 here?

Veer said: (Mar 16, 2020)
The easiest way: A : B = 2 : 1 (work). B = 12. A can finish work 1 --- 12. 2 ---- 6. A+B = 12*6/12+6 = 4.

Manzoor said: (Jul 30, 2020)
No @Veer According to me, the solution is; 2A=B in time. There, the efficiency is inversely proportional to time. Efficiency of A:B = 1:2 Total work is done by B = No of day's * efficiency = 12*2 = 24. If together done the same work= 24÷3. = 8 days. Please correct me, If I am wrong.

Uma said: (Jan 4, 2021)
A=x, B = 2x. 1/x+1/2x = 1/12, 3/2x = 1/12, 3/6 = 2, x = 2. so, B = 2x, 2 * 2 = 4.

Roy said: (Sep 25, 2021)
@All. Given A=2B. B's 1 day work = 1/12, So A's 1 day work=2*1/12=1/6. (a+b)1 day = 1/6 + 1/12 = 1/4, Hence 4 days.

Aditya said: (Jul 12, 2022)
A finished work in 6 days. B finishes work in 12 days. Calculating LCM we get 12 which is total work. Now, work efficiency of A = 12/6 = 2 unit/day, work efficiency of B = 12/12 = 1 unit/day, working together A+B = 2+1 = 3unit/day, Therefore for finishing 12 unit work together they need 12/3 = 4 days.