Question

In a two-digit number, the sum of the digits is 7. The difference of the number obtained by reversing the digits and the number itself is 9. Find the number.

Answer 1

Let x be the digit at ten's place and y be the digit at unit's place.
Then, the number is 10x + y.
Number obtained by reversing the digits = 10y + x
According to given information, we have
x + y = 7     ....(i)
And, (10y + x) - (10x + y) = 9
⇒ 10y + x - 10x - y = 9
⇒ 9y - 9x = 9
⇒ 9(y - x) = 9
⇒ y - x = 1    ....(ii)
Adding eqns. (i) and (ii), we get
2y = 8
⇒ y = 4
⇒x + 4 = 7
⇒x = 3
∴ Required number
= 10x + y 
= 10 x 3 + 4
= 30 + 4
= 34.