Question

A two digit number is obtained by multiplying the sum of the digits by 8. Also, it is obtained by multiplying the difference of the digits by 14 and adding 2. Find the number.

Answer 1

Let the tens digit of the number be x and the units digit be y.
So, the number is 10x + y.
According to the question,
10x + y = 8( x + y ) 
⇒ 10x + y = 8x + 8y
⇒ 2x = 7y                         ....(1)

and 10x + y = 14( x - y ) + 2 or 10x + y = 14( y - x ) + 2
⇒ 4x - 15y = - 2       ...(2)   or 24x - 13y = 2       ....(3)

Solving (1) and (2), We get
y = 2 and x = 7

Solving (1) and (3), We get
y = `2/71`

This is not possible, since y is a digit and cannot be in fraction form.
So, the number is 72.