Question

A number consists of two digits whose sum is 9. If 27 is subtracted from the number its digits are reversed. Find the number.

Answer 1

Let a digit of two digit number be x. 

The sum of two digits = 9 

∴ Another digit = 9 – x 

The number = 10 (9 – x) + x 

= 90 – 10x + x 

= 90 – 9x 

If 27 is subtracted from the number its digits are reversed. 

∴ (90 – 9x) – 27 = 10x + (9 – x) 

63 – 9x = 9x + 9

9x + 9x = 63 – 9 

18x = 54 

∴ x = \(\frac{54}{18}\) = 3 

∴ Units digit = 3 

Tens digit = 9 – 3 = 6 

∴ The number = 63