In this question the sum of two digit number and the number obtained by interchanging the digits exceeds, the given number is given.

You have to find the number.

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

This is the Question Number 13 Of Exercise 3E of RS Aggarwal Solution.

# The Sum of the digits of a two-digit number is 15. The number obtained by interchanging the digits exceeds, the given number by 9. Find the number.

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Let the number be xy.

Given,the sum of the digits of a two digit number is 15.

x+y = 15 …(1)

Also, if the digits are interchanged the result exceeds the original number by 9.

10y+x=10x+y+9

10y+x-10x-y=9

9y-9x=9

y-x=1 …(2)

(1)+(2) => 2y = 16

y = 16/2 = 8

(1) => x+8=15

x=15-8=7

Therefore the given number is 78