Question

Eight times a two - digit number is equal to three times the number obtained by reversing the older of it's digits. If the difference between the digit is 5. Find the number

Answer 1

Let us assume, x and y are the two digits of a two-digit number and y > x

Therefore, the two-digit number = 10x + y and reverse number = 10y + x

8 (10x + y) = 3 (10y + x)

80x + 8y = 30y + 3x

77x = 22y

7x = 2y -----------------1

Also given:

y – x = 5

x =  y - 5 --------------2

Substitute the value of x from equation 2 in equation 1

7 (y - 5) = 2y

7y – 35 = 2y

5y = 35

y = 7

and x = y – 5 = 7 – 5 = 2

Therefore, the two-digit number = 10x + y = (10 * 2 + 7) = 27