This question is from linear equations in two variables in which we have been asked to find the number if the sum of a two digit number and the number obtained by reversing the order of the digits is 121 and if the digits differ by 3.

Kindly give me a detailed solution of this question

RS Aggarwal, Class 10, chapter 3E, question no 18

## Let the two digit number be 10x+y

On reversing its digits, we get the number 10y+x

Given, (10x+y)+(10y+x)=121

11x+11y=121

=> x+y=11 — (1)

Given, x−y=3 — (2)

Adding (1) and (2), we get

2x=14 => x=7

Substituting x=7 in the equation (2), we get 7−y=3⇒y=4

Hence, the number is 74 or 47