Question

A two digit number is 4times the sumof its digit. If 18 is added to the number the digit .find the number

Answer 1

Let the digits be x and y.

Then the number is 10x + y

10x + y = 4(x + y) = 4x + 4y.

Thus, 6x = 3y or y = 2x.

If 18 is added to the number, the digits are reversed. Adding 18, we get.

10x + y + 18 = 10y + x

or 9y - 9x = 18.

Substituting the value of y = 2x in the above equation, we get

9*2x - 9x = 18.

18x - 9x = 18 or 9x = 18.

Thus, x = 2.

Since y = 2x, y = 4.

Thus, the number is 24.