Question

The sum of digits of a two digit number
is 15. The number obtained by interchanging the digits exceeds the given number by 9. Find the number

Answer 1

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 

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Answer 2

let ones digit be x

tens digit be y

no. = x+10y

reversing no. =10x+y

a/q

x+y = 15 ---i)

again

10x+y = x+10y+9

9x-9y= 9

9(x-y) = 9

x-y = 1--------'ii

fromi)&ii

x+y =15

x-y = 1

on solving

2x=16

x= 8

x-y = 1

8- y = 1

-y = -7

y =7

no= x+10y

= 8 + 10 ×7

= 78