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Question

The sum of the digits of a two-digit number is 7. If the number formed by interchanging the digits is less than the original number by 27, then find the original number.


A

43

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B

61

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C

52

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D

25

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Solution

The correct option is C

52


Given, the sum of the digits of a two-digit number is 7.

Let the units digit of the original number be x.


Then, the tens digit of the original number is 7x.

The two-digit number =10(7x)+(1×x)
=7010x+x=709x

When the digits are interchanged, the new number is 10(x)+1(7x)=10xx+7=9x+7

New number = Original number - 27

9x+7=709x2718x=36x=2

The tens digit =7x=72=5

The original number is 52.


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