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A two – digit number is such that the ten’s digit exceeds twice the unit’s digit by 2 and the number obtained by interchanging the digits is 5 more than three times the sum of the digits. Find the two-digit number.

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answer is A.

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Detailed Solution

Concept- We can take two-digit numbers such as

, where x is a digit in the tens place and y is a digit in the unit place, and form the required equation from the above data. Interchanging the digits means writing the number as

, where y is the tenth digit and

x

is the unit digit.
Consider the two-digit number as

.
According to the question,

and

When solving (2) and (1), we get

Now,

Therefore, the two-digit number is 83.
Hence, the correct answer is option 1) 83.
of a Linear Equation
of a Linear Equation

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