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Question

The digit at tens place of a two digit number is two times the digit at its units place. If the digits are interchanged and added to the original number, then the result will be 66. Find the original number.

A

42

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B

63

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C

84

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D

21

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Solution

The correct option is A 42 Let the digit in units place be x. Then, the digit in tens place will be 2x. So, the number will be (10×2x)+(1×x)=20x+x=21x When we interchange the digits, the number will be (10×x)+(1×2x)=10x+2x=12x It is given that, 21x+12x=66 ⇒ 33x=66 ⇒ x=6633 ⇒ x=2 ∴The digit in units place =2 The digit in tens place =4 The original number is 42. Verification: Original number =42 Interchanging the digits of 42, we get 24. Sum of the original number and the interchanged number is 42+24=66.

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