The sum of digits of a two digit number is 15. The number obtained by reversing the order of digits of the given number exceeds the given number by 9. Find the given number.

Question

Philoid · Accepted Answer

Let the unit’s digit be a and tens digit be b.

Number = 10b + a

Reverse of the number = 10a + b

Given, sum of digits of a two digit number is 15.

⇒ a + b = 15 ------ (1)

Also, the number obtained by reversing the order of digits of the given number exceeds the given number by 9.

⇒ 10a + b – 10b – a = 9

⇒ a – b = 1 ------- (2)

Solving (1) and (2), we get

⇒ a = 8 and b = 7

The number is 78.