Aptitude - Numbers - Discussion

All explanation is very good. Thanks to all. @Rahaman your formal also nice.

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.

Please explain in any other way.

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.

@Ashwini why you consider 23 only as example?

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.

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.

The difference of two numbers is 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.

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.