Question

A number consists of two digits whose sum is 8. If 18 is added to the number, its digits are reversed, find the number?

Answer 1

x + y = 8

10x + y + 18 = 10y + x
9x - 9y = -18
9(x - y) = -18
x - y = -2

x + y = 8
x - y = -2
2x = 6
x = 3
y = 5

number is 35.

Answer 2

Hey !

Let the no: in unit's place be "y" and the no: in ten's place be "x"
The original no: would be "10x+ y"

Given:-

x + y = 8                   ----->(1)

When 18 is added to the original no: , the digits get reversed [ 10y + x is the reversed no:]
10x + y + 18 = 10y + x

10x - x + y - 10y = -18

9x - 9y = -18

9 [ x - y ] = -18

x - y = -2             ---------------> (2)       

Adding equations 1 and 2 ,

x + y = 8
x - y = -2
--------------
2x = 6

x = 6/2 = 3

x + y = 8

3 + y = 8

y = 8 - 3

y = 5

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x = 3 , y = 5

The no: is 10(3) + 5 = 35

35 is the required no: