A number consists of two digits whose sum is 9. If 27 is subtracted fr

1.	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» 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

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»

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