Question

Eight times a two digit number is equal to three times the number obtained by reversing the order of its digits. If the difference between the digit is 5, find the number.

Answer 1

Let the digits of the number be x and y, with x being the number in the tens place and y being the number in the units place.

Let y > x, then y - x = 5.

So, the number is 10x + y.

Then, 8*(10x+y) = 3*(10y+x)

This gives, 80x + 8y = 30y + 3x

Or 77x = 22y

This gives, 7x = 2y or y = 7x/2.

Substituting the value of y = 7x/2 in y - x = 5, we get

7x/2 - x = 5

or 7x-2x = 10

Thus, 5x = 10 or x = 10/5 = 2.

And y = 7 * 2 / 2 = 7.

Thus, the number is 10 * 2 + 7 = 27.