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Question

In a two-digit number, the units digit is twice the ten's digit. Also, if 27 is added to the number, the digits interchange there places. Find the number.


A

40

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B

52

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C

28

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D

36

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Solution

The correct option is D

36


Let the digit in the units place be x and digit in the tens place be y.
Units digit = twice the tens digit [Given]
x = 2y . . . . (1)
Let the two digit number be 10y + x.
Number obtained by reversing the digits = 10x + y
Number + 27 = Number obtained by interchanging the digits [Given]
10y + x + 27 = 10x + y
9x9y=27
xy=3 . . . . (2)
Putting x = 2y in equation (2), we get,
2y - y = 3 y = 3
Putting y = 3 in equation (2), we get,
x - 3 = 3 x = 6
10y + x = 10 × 3 + 6 = 36
Hence, the number is 36.


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