Question

The tens digit of a two-digit number is 5 greater than the units digit. If you subtract twice the reversed number from the original number, the result is a fourth of the original number. Find the original number

Answer 1

The number is 72.

Explanation:

Let the number be xy.

x = y + 5

10x + y - 2(10y + x) = 0.25(10x + y)

10x - 2x + y - 20y = 2.5x + 0.25y

5.5x - 19.25y = 0

Substituting for x:

5.5y + 27.5 - 19.25y = 0

-13.75y = -27.5

y = 2.

So x = 2 + 5 = 7.