Question

The sum of digits of a two digit no. is 15.The no. obtained by reversing the order of digits of the given no. exceed the given no. by 9.Find the given no..

Answer 1

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 

Answer 2

Hey friend...!! here's your answer
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Let the unit digit = x
ten's digit = y

x + y = 15-----------1

According to question,

10x + y + 9 = 10y + x
10x - x + 9 = 10y - y
9x + 9 = 9y
9x - 9y = -9
x - y = -1 ---------------2

By elimination Method ,

x + y = 15
x - y = -1
- + +
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2y = 16

y = 8

Put the value of y in equation 1

x + 8 = 15
x = 7

So that the number is 78

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