Question

2. The sum of the digits of a two-digit number is 11. If 63 is subtracted
from the number, the digits get interchanged. What is the number?
(1) 38 (2) 83 (3) 92 (4) 29​

Answer 1

Answer :-

Let the unit's digit be x and ten's digit be y

Number = 10y + x

It is given that, sum of digits is 11

→ x + y = 11

Number obtained by reversing the digits = 10x + y

According to the question :-

→ 10y + x - 63 = 10x + y

→ 10y - y - 63 = 10x - x

→ 9y - 63 = 9x

→ 9y - 9x = 63

→ 9 ( y - x ) = 63

→ y - x = 63 / 9

→ y - x = 7

Now, we have 2 equations :-

→ x + y = 11

→ y - x = 7

Adding both the equations :-

→ x + y + y - x = 11 + 7

→ 2y = 18

→ y = 18 / 2

→ y = 9

→ x + y = 11

→ x + 9 = 11

→ x = 2

Number = 9 × 10 + 2 = 92

Number = 92