Aptitude - Numbers - Discussion

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.

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.
y = 270.

Let Y is the larger Number and X is the smaller Number.
The difference between X and Y is 1365.
Also, 6 times X is equal to Y - 15.

So, if we subtract 15 more from 1365 we get the difference of 6 times X and X as :

6X - X = 1365-15.
X = 270.
Y = 1635.

Let us assume x as smaller number and y as the bigger one.

So, from the question,
y-x = 1365 --->1
y = 1365 + x --->2
From question,
y/x = 6 --->3
Gives, y = 6x. --->4

Sub 4 in 1,
6x - x = 1365
x = 273.

(Since leaves remainder 15 which is 5 ×3 =15. So, subtracting 3 from 273 to get the number that leaves no remainder)
So the number that leaves no remainder is 270.

Thanks for explaining the answer @Pooja.

225 is the correct answer.
1365 - 15 = 1350.
So, 225 * 6 is 1350, and the remainder is 15. So, kindly calculate the sum with the answer.

Difference of two numbers:
a- b = 1365.
a/b = 6 15/b.

a - b means 1 times of a is reduced from b and 15 extra part is remaining.
Also it is given that 6 times of b is leaving 15 as remainder;
So in a - b we only have 5 times b + 15.

Thus 1365-15/5 is the smallest number.
1365-15/5= 270.

For example
If a = 117 b = 17,
a-b = 100,
6b = 102,
5b = 85,
a/b leaves remainder 15.
So, a-b-15=85 which is equal to 5b.