Sum of the digits of a two-digit number is 9. When we interchange the digits, it’s found that the resulting new number is greater than the original number by 27. What is the two-digit number?

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answer is D.

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Detailed Solution

Forming the mathematical equation according to the condition we find

The digit formed with a being the tenth place digit and b being the unit placed digit is

It’s also given that if we interchange the digits then the resulting new number is greater than the original number by 27.
The digit formed with b being the tenth place digit and a being the unit placed digit is

The difference is 27. So,

Simplifying the equation, we get
Question Image

Now we have two equations of linear form of a and b. We solve them to find the values of a and b.
From equation (ii) we have the value of b and we place that in equation (i).
Question Image

Putting the value of a in equation (ii) we get

So, the original number is 36.
So, option 4 is correct.

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