Question

The sum of the digits of a two digit number is 7. When 27 is subtracted from the number the digits of the number gets reversed. What is the original number?

• A. 16
• B. 61
• C. 25
• D. 52

Answer 1

The correct option is D

52

Given sum of the digits is 7. So, if the digit in the unit’s place is x, then the ten’s place digit will be 7 – x.

So, the number = 10(7 – x) + x.
After reversing the digits the number will be 10x + (7 – x).

ATQ,
Original number - 27 = Reverse number
10(7 – x) + x – 27 = 10x + (7 – x)

70 - 10x + x – 27 = 10x + 7 – x

43 – 9x = 9x + 7

43 – 7 = 9x + 9x

18x = 36

x = 36 $÷$ 18 = 2

$\therefore$ The number is 52.