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# The sum of a two-digit number and the number obtained by reversing the order of its digits is 121, and the two digits differ by 3. Find the number.

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An Important question based on Linear Equations in two Variables Chapter of R.S Aggarwal book for ICSE & CBSE Board.
Here the sum of a two-digit number and the number obtained by reversing the order of its digit and the two digits differ by is given.
you have to find the number.
This is the Question Number 18 Exercise 3E of RS Aggarwal Solution.

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1. Let x be the ones digit and y be the tens digit.

Then

Two digit number before reversing = 10y + x

Two digit number after reversing = 10x + y

As per the question (10y + x) + (10x + y) = 121

⇒11x + 11y = 121

⇒x + y = 11 …….(i)

Since the digits differ by 3, so

x – y = 3 ……….(ii)

Adding (i) and (ii), we get

2x = 14

⇒ x = 7

Putting x = 7 in (i), we get

7 + y = 11

⇒ y = 4

Changing the role of x and y, x = 4 and y = 7

Hence, the two-digit number is 74 or 47.

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