The sum of the digits of a two digit number is 7. When 27 is subtracted from the number the digits of the number will reverse.

What is the original number?

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Solution

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.

Then the number will be 10(7 – x) + x. After reversing the digits the number will be 10x + (7 – x).

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 $\div$ 18 = 2

$∴$ The number is 52.

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

The sum of the digits of a two digit number is 7. When 27 is subtracted from the number the digits of the number will reverse.

What is the original number?