Question

The sum of digit of a 2-digit number is 7 .if 27 is added to the number ,the digit interchange their places .find the number

Answer 1

Hello !

Let the digit in unit's place be "y" and the digit in ten's place be "x"

Then the two digit no: is 10x + y

A.T.Q.,

x + y = 7 -----> (1)


also,
When digits are interchanged the no: is --> 10y +x

10x + y + 27 = 10y + x

10x - x + y - 10y = -27

9x - 9y = -27

9(x- y) = -27

x - y = -3 ----> (2)
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Adding (1) and (2) ,

x + y = 7
x - y = -3
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2x = 4

x = 2


x + y = 7

2 + y = 7

y = 7 -2

y = 5
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10x + y ---> 10(2) + 5 = 25

The no: is 25