Question

The sum of the digits of a two-digit number is 15. The number obtained by interchanging the digits exceeds the given number by 9. The number is ______.

Options

• 96

• 69

• 87

• 78

Answer 1

The sum of the digits of a two-digit number is 15. The number obtained by interchanging the digits exceeds the given number by 9. The number is 78.

Explanation:

Let the ten’s digit = x and unit’s digit = y. 

Then x + y = 15 and (10y + x) – (10x + y) = 9

⇒ 9(y – x) = 9

⇒ y – x = 1

So, y = x + 1.

Substitute: x + (x + 1) = 15

⇒ 2x = 14

⇒ x = 7, y = 8

The original number = 10x + y = 78.