Question

Seven more than a 2-digit number is equal to two less than the number obtained by reversing the digits. The sum of the digits is 5. 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
(10x + y) + 7 = (10y + x) - 2
⇒ 10x + y + 7 = 10y + x - 2
⇒ 9x - 9y = -9
⇒9(x - y) = -9
⇒ x - y = -1     ....(i)
Also, x + y = 5    ....(ii)
Adding eqns. (i) and (ii), we get
2x = 4
⇒ x = 2
⇒ 2 + y = 5
⇒ y = 3
∴ Required number
= 10x + y
= 10 x 2 + 3
= 20 + 3
= 23.