This is the Important question based on Linear Equations in two Variables Chapter of R.S Aggarwal book for ICSE & CBSE Board.

Question Number 11 Exercise 3E of RS Aggarwal Solution

Here the sum of two digit number and the number obtained by interchanging its digits exceeds by the given number is given. you have to find the number.

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# The sum of two digits of a two-digit numbers is 12. the number obtained by interchanging its digits exceeds the given number by 18. Find the number.

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Let us assume x and y are the two digits of the number

Therefore, two-digit number is = 10x + y and the reversed number = 10y + x

Given:

x + y = 12

y = 12 – x ———–1

Also given:

10y + x – 10x – y = 18

9y – 9x = 18

y – x = 2 ————-2

Substitute the value of y from eqn 1 in eqn 2

12 – x – x = 2

12 – 2x = 2

2x = 10

x = 5

Therefore, y = 12 – x = 12 – 5 = 7

Therefore, the two-digit number is 10x + y = (10*5) + 7 = 57