Discussion :: Numbers - General Questions (Q.No.13)
Numbers - Important Formulas
«« Numbers - General Questions
13.
The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ?
[A].
240
[B].
270
[C].
295
[D].
360
Answer: Option B
Explanation:
Let the smaller number be x. Then larger number = (x + 1365).
x + 1365 = 6x + 15
5x = 1350
x = 270
Smaller number = 270.
Shoeb said: (Dec 15, 2010)
Why the larger no is added. since there is a difference of two numbers in question.
Janu said: (Dec 29, 2010)
@shoeb if x-y=1365
then y=x+1365
here in this problem they assumed x is d smaller and y is d larger one..
got it...
Seema said: (Jan 21, 2011)
why x is multiplied to 6?
Ashwini said: (Feb 1, 2011)
x is smaller no.
Seema i think you will get after this:
after multiply to 6(quotient) we get original no.
e.g 2)23(11 - 2 ------ 03 2 ------- 1
so 2*11=22 & after adding reminder i.e 1 into 22 we get 23.
Raj said: (Feb 18, 2011)
How you got 6X+15 ?
Rajesh said: (Mar 12, 2011)
I can't understand "6x+15" this step, why x is multiplied with 6? Can anybody help me?
Shraddha said: (Apr 29, 2011)
It is done through formula:- dividend=(divisor*quotient)+remainder Here,divisor=X(smaller no.)
quotient=6
remainder=15
Shivam Bajaj said: (Jun 15, 2011)
Why m i gettin 225 ??? 6*225=1350 and remainder is 15 and quotient is 6 ....in that case it matches up small number which is 225 ....
Jomon said: (Jun 17, 2011)
y-x=1365 y=1365+x
y/x-15=6 y-15=6x y=6x+15 x + 1365 = 6x + 15 5x = 1350 x = 270
Smaller number = 270.
Meenu said: (Dec 28, 2011)
Good Explanation Jomon... Good Explanation Ashwini..;
Thanks:-)
Deiva said: (Feb 21, 2012)
I can't understand "5x=1350" this step,please explain
Jhabar said: (Mar 15, 2012)
Thanks jomon, thanks sradha.
Rahaman said: (Mar 21, 2012)
(diff-rem)/qut-1=small num so
(1365-15)/6-1=270
Raj said: (Jun 2, 2012)
Let the larger number is x and smaller is y.
Now x-y=1365....(1)
Again dividend=divisor*quotient+remainder
Therefore x=6y+15 put in ..(1)
6y+15-y=1365
or 5y=1350
or y=270
Hence answer is (b)270
Abhi said: (Jun 21, 2014)
Here x+1365 = 6x+15. 1365-15 = 6x-1x. 1350 = 5x. x = 1350/5.
x = 270.
Abhijeet Patil said: (Jul 30, 2014)
x = larger number.
y = smaller number. Given that,
x-y = 1365...... (1). x/y = 6.
x = 6y+15.
x-6y = 15....... (2). Solving eq 1 and 2. x-6y = 15 -x+y = -1365
_____________
-5y= -1365
Lets say x is greater number and y is smallest number.
So first condition is x-y = 1365. So second condition is y/x gives 6 as a quotient and 15 as a remainder. According to formula (dividend)=(divisor*quotient)+remainder.
So x = 6y+15. Putting x = 1365+y from first condition
y = 270.
Which is smaller number.
P.Janaki said: (Oct 11, 2014)
The difference of two numbers is 1365.
Bharath said: (Dec 16, 2014)
Let the two numbers be x and y (x > y). The difference between first and second number is 1365. x - y = 1365...............(1). When first number is divided by second 6 is the quotient and 15 is the remainder. This is written as: x / y = 6 15/y (i.e. a mixed fraction).
x / y = (6y+15)/y (on simplifying the mixed fraction). x = 6y + 15......................(2). Solving (1) and (2), we get.
y = 270 ; x = 1635.
Manish Kumar Rai said: (Mar 12, 2015)
Let the larger number is: X. And the smaller number is: Y. Now the relation one will be according to question. (X-Y) = 1365....(i). And other relation will be: As we know that Dividend = Quotient*Divisor+Remainder; We are given with Quotient = 6. && Remainder = 15. Larger number = X = Dividend; And Smaller number = Y = Divisor. Now the equation will be: Dividend = Quotient*Divisor+Remainder. X = 6*Y+15. X = 6Y+15.....(ii). Now putting the value of X in equation (i) we get. (X-Y) = 1365. (6Y+15-Y) = 1365. (5Y+15) = 1365. 5Y = 1350.
Y = 270 which is our Answer.
Sana said: (Apr 26, 2015)
@Ashwini why you consider 23 only as example?
Gadha said: (Jun 12, 2015)
Difference of 2 number is 1365 and if add 1365 to that a number (x+1365) is equal to other number that is = (6x+15).
2. How can find it biggest or smaller so that you can figure it if you add something to smaller than it become equal to other number x+1365=6x+15.
Sesi said: (Aug 1, 2015)
Please explain in any other way.
Sangeetha said: (Sep 7, 2015)
a-b = 1365.
a/b = Q => 6 and 15 as R. (b*6)+15 = a.
(b*6)+15 = 1365+b. (b*6) - b = 1350.
6b-b = 1350. 5b = 1350.
b = 270.
Rnvardhini said: (Sep 15, 2015)
All explanation is very good. Thanks to all. @Rahaman your formal also nice.
Sandy said: (May 23, 2016)
The solution is wrong it doesn't satisfy the condition. As per solution smaller number is 270 so, when you divide larger number i.e. (1365 - 270 = 1095).
Then, 1095/270 is not equal to 6.
Rahul said: (Jun 7, 2016)
@Jomon.
Good explanation, thanks.
Alamin said: (Jul 23, 2016)
Very good explanation @Raj.
Keerthy said: (Sep 6, 2016)
Thanks @Vinni.
Ashok Pathi said: (Sep 14, 2016)
Thanks @Rahaman.
Sooraj Abi said: (Jan 25, 2017)
Thanks for the explanation @Rahaman.
Venkat.K said: (Feb 7, 2017)
Good explanation @Jomon.
Krish said: (Aug 8, 2017)
Can we simply apply this,
x-y = 1365.
x\y = 6 (is it necessary to add remainder with it).
Pradeep Chauhan said: (Aug 11, 2017)
How you get x/y-15=6?
Tejas said: (Nov 8, 2017)
Difference between two natural nos is 23. If we get quotient 2 on dividing the bigger no by the smaller no then find the nos.
Smooth Kill said: (Jan 19, 2018)
It's simple. lets take the larger number = (x) and smaller number = (y)
the difference between them is 1365
x-y = 1365 ---------- equation 1.
we know dividend = quotient * divisor + remainder
here the larger number is divided by smaller number
hence we get ,
6x + 15 = y
arranging it we get
6x - y = -15 ----------- equation 2.
adding both equation and solving them we get
y = 270.
Raju Reddy said: (Feb 8, 2018)
Two numbers Difference is given I. e. 1365 one number =X(large) and another number(small)=Y.
X-Y=1365. Large number divided by small number i.e
X/Y.....Y)X(6 /15 X=6Y+15 (above eqn. X-Y=1365then X=1365+Y).
1365+Y=6Y+15.
1365-15=6Y-Y i.e 1350=5Y.
Y=1350/5 i.e 270.
In problem asked smaller number that's why the ans is 270.
Udit said: (Mar 11, 2018)
@Seema.
6 is quotient.
Abhishek Gupta said: (Jun 19, 2018)
I can't understand this question, anyone can help me to solve this problem, please.
Vishan Dogra said: (Dec 6, 2018)
Larger no is y. y-x= 1365 ---> 1.
Divident =divisor * q+R.
y=x * 6 + 15,
Y=6x + 15 ---> 2 Substitute the value of eq 2 in 1.
6x + 15 - x = 1365, 5x + 15 = 1365,
5x = 1365-15,
x = 1350/5 = 270.
Bharath said: (Dec 14, 2018)
Dividend = (divisor * quotient) + remainder. Let the smaller number be x. Then larger number = (x + 1365).
On dividing larger number by smaller number. => (x+1365)/x.
x + 1365 = 6x + 15,
5x = 1350,
x = 270.
Smaller number = 270.
Paimon Dkhar said: (Jan 13, 2019)
X is the smaller and y is the larger. Y=x+1365,
Y=270+1365,
Y=1635.
Larger divided by a smaller number. =1635/270. Here I got 6 quotient & 15 Remainder.
Yes, 270 is the smaller number.
Pooja said: (Apr 1, 2019)
Let the smaller number be= x.
Then the larger number be= x+1365. We already have,
Quotient = 6,
Remainder= 15,
Divisor = x ( as in every division divisor is smaller than the dividend),
Dividend = x+1365. As per formula,
Divisor = (dividend-remainder)/quotient. => x = (x+1365-15)/6,
=> x = (x+1350)/6,
=> 6x-x = 1350,
=> 5x = 1350,
=> x = 1350/5,
=> x = 270 (the smaller number) (answer).
Anudeep Gajjala said: (Apr 20, 2020)
Good explanation, Thanks @Jomon.
Sania Prathi said: (Jul 13, 2020)
Nice explanation @Jomon.
Aishwarya said: (Aug 21, 2020)
@All. Lets consider smaller number as X --->(i)
As per given difference of two numbers is 1365. So consider larger number as X+1365 ---> (ii). Dividend = quotient * divisor + remainder.
On dividing larger number by smaller number just put given values in above formula.
So we got equation as:
X+1365 = 6 * X + 15
5X = 1350.
X = 270 is smaller number.
Uma said: (Oct 18, 2020)
Perfect and good explanation Thanks @Bharath.
Uma said: (Oct 18, 2020)
Let us assume the largest number is X & the Smallest number is Y. The difference between two number is 1365. So, X - Y=1365
X=1365+Y------------(1). Now, assume the largest number is dividend, the smaller number is divisior
So, X is dividend & Y is divisior.
We know that, Dividend= divisior*quostient + remainder.
X = Y * 6 + 15.
X = 6Y + 15------------> (2). Let substitute eq(1) in eq(2).
1365 + Y = 6Y + 15.
Y - 6Y = 15 - 1365.
- 5Y = - 1350. Here minus(-) minus(-) gets cancel. So, 5Y = 1350.
Y= 1350/5.
Y=270.
Bhushan J said: (Dec 29, 2020)
Let smaller no x. Larger no x + 1365.
Quotient = 6.
Remainder = 15
Divisor = x + 1365,. Dividend = x,
Dividend = divisor * quotient + remainder.
x + 1365 = x * 6 + 15,
1350 = 5x,
x = 270.
Srikanth said: (Sep 4, 2021)
Let's assume; x is the larger number.
y is smaller number. x - y = 1365
x/y = 6
x = 6 * y + 15,
6 * y + 15 - y = 1365.
![Why was the [drive] block used instead of the [drive for] block in this project?](https://ap.cdnki.com/r_why-was-the-drive-block-used-instead-of-the-drive-for-block-in-this-project---2375f680d421ae5f22a98dc737dd4dfc.webp)
