Question

A number consists of two digits whose sum is 9. If 27 is added to the number, the digits change their places. Find the number.

Answer 1

Given: Let the ten’s digit = x and unit’s digit = y. Then x + y = 9 and the number = 10x + y. Adding 27 gives the reversed number 10y + x.

Step-wise calculation:

1. 10x + y + 27 = 10y + x

2. 9x – 9y + 27 = 0

⇒ Divide by 9

⇒ x – y + 3 = 0

3. So, x – y = –3, i.e., x = y – 3.

4. From x + y = 9 substitute x:

(y – 3) + y = 9

⇒ 2y – 3 = 9

⇒ 2y = 12

⇒ y = 6

5. Then x = 9 – y = 3.

The number = 10x + y

= 10 × 3 + 6 

= 36

6. Check: 36 + 27 = 63, which is 36 with digits reversed.

The required number is 36.