A number consists of two digits whose sum is 11. If 27 is added to the number, then the digits change their places. What is the number?

Options

A. 47
B. 65
C. 83
D. 92

Answer

A

Explanation

Let the ten.s digit = x
Then, unit.s digit = `(11-x) `
So, number = `10x + (11 – x)= 9x + 11. `
According to the question
`(9x + 11) + 27 = 10 (11 - x) + x `
or, `9x + 38 = 110 - 10x + x `
or, `18x = 110 -38 `or, `x = 72/18 = 4`
So, ten.s digit = 4 and
Unit.s digit = `(11 – x)= (11 – 4) = 7`
So, Required number = `(9x + 11) = (9 xx 4 + 11) = 47`.