Question

the sum of the digits of a two digit number is 5 on adding 27 to the number its digits are reversed find the original number

Answer 1

Let the number be 10x+y
where x+y=5--------Statement 1
Now number obtained after interchanging digits=10y+x
So According To The Question:
10x+y+27=10y+x
9x+27=9y
Now Computing Statement 1
x+y=5
y=5-x

9x+27=9(5-x)
9x+27=45-9x
18x=18
x=1
Now x=1 So according to statement 1 y= 4
Hence original number is 14

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Answer 2

Let the digits be x and y respectively.

Therefore, x + y = 5 ----------- (1)

Original Number : 10x + y

Reversed Number : 10y + x

10x + y - (10y + x) = 27

10x + y - 10y - x = 27

9x - 9y = 27

9 (x - y) = 27

x - y = 3 ------------ (2)

Adding equation (1) and (2)

2x = 8

x = 4

Substituting value for x in equation (1), we get

4 + y = 5

y = 1

The numbers are 41 and 14.