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

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

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).

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