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Q.

The sum of the digits of a 2 digit number is 7. The number obtained by interchanging the digits exceeds the original number by 27. The number is ____.

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Detailed Solution

Concept- Using both digits as independent variables, we create two equations: one deals with the addition of two digits, and the other deals with the relation that the number is exceeded by 27 when two digits are interchanged. We employ the idea of writing a number in a generic fashion while being aware of its location as one or tenths.
Let digit at ones place

and
Digit at tens place

So, the number will be

Reverse digit will be represented as,

So,

Adding equation (1) and (2)

Substituting in equation (1)

Hence, the number will be 25

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