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Question

# The digits of a two digit number differ by 2. If the digits are interchanged and resulting number is added to the original number we get 88. What is the original number?

A

24

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B

42

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C

57

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D

53

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Solution

## The correct option is D 53 Given : The difference between the digits is 2. So, if unit's place digit is x then ten’s place will be x + 2,then the number will be 10(x + 2) + x. After reversing the digit the number will be 10x + x + 2. 10(x + 2) + x + 10x + x + 2 = 88 (given) 10x + 20 + x + 10x + x + 2 = 88 22x + 22 = 88 22x = 88 - 22 = 66 x = 66 ÷ 22 = 3 ∴The number is 53.

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