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If we add the square of the digit in the tens place of a positive two digit number to the product of the digits of that number we shall get 52 and if we add the square of the digit in the units place to the same product of the digits we shall get 117. Find the two digit number.

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answer is C.

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Detailed Solution

Let a be the digit on the unit's place and b on ten’s place.
the square the digit in the tens place of a positive two digit number

product of the digits of that number

the square of the digit in the units place

same product of the digits

Now we know the identity that

Now we have to find two numbers a and b such that their sum is 13 and the difference is 5.
Because, 9+4=13 and 9-4=5
Hence the two digit number is 49.

So, option 3 is correct.

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