Question

The sum of a two-digit number and the number obtained by interchanging the digits is 154. If the ten’s digit is 2 more than unit’s digit, find the original number.

Answer 1

Let the unit’s digit be x,

Then the ten’s digit = x + 2,

Original number = 10(x + 2) + x = 11x + 20,

Reversed number = 10x + (x + 2) = 11x + 2,

Given: (Original) + (Reversed) = 154,

(11x + 20) + (11x + 2) = 154

22x + 22 = 154

22x = 154 − 22

22x = 132

x = `132/22`

∴ x = 6

Thus,

Unit’s digit = x = 6

Ten’s digit = x + 2 = 8

So, the original number = 86

Here,

Reversed number = 68

Sum = 86 + 68 = 154

Ten’s digit (8) is indeed two more than the unit’s digit (6).

Hence, the required number is 86.