Aptitude - Numbers - Discussion

I can't understand this question, anyone can help me to solve this problem, please.

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.

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.

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.

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).

Good explanation, Thanks @Jomon.

Nice explanation @Jomon.

@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.

Perfect and good explanation Thanks @Bharath.

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.