Question

The sum of the digits of a 2-digit number is 14. The number obtained by interchanging its digits exceeds the given number by 18. Find the number.

Answer 1

Let unit digit = x

and tens digit = y

then, number = 10y + x

Also number obtained after interchanging its digit = 10x + y

According to question,

x + y = 14         ...(i)

10x + y − (10y + x) = 18

⇒ 9x − 9y = 18

⇒ x − y = 2         ...(ii)

From eqn. (i) + (ii), we have

x + y = 14

x − y = 2

2x = 16

x = 8

So, y = 14 − 8 = 6      ...[from (i)]

thus, Required number = 10y + x

= 10 × 6 + 8

= 68