Question

A number consists of two digits whose sum is 9. If 9 is subtracted from the number, the digits interchange their places . Find the number​

Answer 1

Answer: The number is 54.

Step-by-step explanation:

Let x and y be the digits of the number at ten's place and unit's place respectively.

According to the question,

1st equation: x + y = 9

2nd equation: 10x + y - 9 = 10y + x

From 1st equation,

x = 9 - y

Substituting x = 9 - y in 2nd equation..

10(9 - y) + y - 9 = 10y + (9 - y)

90 - 10y + y - 9 = 9y + 9

81 - 9y = 9y + 9

72 = 18y

∴ y = 4

And x = 9 - 4 = 5

Therefore, the number = 10x + y = 10(5) + 4 = 54