In a two digit number the sum of the two digits is 8. If 18 is added to the number it's digits are reversed. Find the Number
Answers
Step-by-step explanation:
Let the two digit number be 10x + y where x is the tens digit and y is the units digit.
x + y = 8 (1)
10x + y + 8 = 10y + x
10x - x + y - 10y + 8 = 0
9x - 9y = -8 (2)
Multiplying equation (1) by 9, we get
9(x + y) = 9(8)
9x + 9y = 72 (3)
Adding (2) and (3), we get
9x + 9x - 9y + 9y = -8 + 72
18x = 64
x = 64/18
x = 32/9
Putting x = 32/9 in (1) , we get
32/9 + y = 8
32 + 9y = 72
9y = 40
y = 40/9
The number will be = 10x + y
= 10(32/9) + 40/9
= 320/9 + 40/9
= 320+40/9
= 360/9
= 40
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