Question

Sum of the digits of a two-digit number is 11. The given number is less than the number obtained by interchanging the digits by 9. Find the number.

Answer 1

Let the unit’s digit be x.

Then, the ten’s digit = 11 – x

∴ Number = 10(11 – x) + x

= 110 – 10x + x

= 110 – 9x

Number obtained by interchanging the digits

= 10x + (11 – x)

= 9x + 11

According to the question,

9x + 11 – (110 – 9x) = 9

⇒ 9x + 11 – 110 + 9x = 9

⇒ 18x = 9 – 11 + 110

⇒ 18x = 108

⇒ x = `108/18`

⇒ x = 6

Hence, unit’s digit = 6 and ten’s digit = 11 – 6 = 5

Therefore, the required number is 56.