# Aptitude - Numbers - Discussion

### Discussion :: Numbers - General Questions (Q.No.13)

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

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 y = 270.

 Vinni said: (Oct 5, 2014) Dividend = Divisor*Quotient + Remainder.

 Vinni said: (Oct 5, 2014) Smaller = x. Larger = 1365+x. We have, Dividend = 1365+x. Divisor = x. Quotient = 6. Remainder = 15. Dividend = (divisor*quotient)+remainder. So, 1365+x = (x*6)+15.

 Sudarshan said: (Oct 7, 2014) 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.