Question

the difference between a two digit number and the number obtained by inter -changing the digits is 27 .what is the difference between the digits of the number ?

Answer 1

Lets write this 2-Figure-Number as "xy"

Then the two given conditions give the two equations

A: x + y = 9

and

B: 10x + y - 63 = 10y + x

By subtracting y on both sides of A we obtain an expression for x

A' x = 9 - y

which we use in B, giving the Equation B' which contains as unique variable y:

B': 10(9 - y) + y - 63 = 10y + (9 - y)

or

B': 90 - 10y + y - 63 = 10y + 9 - y

27 - 9y = 9y + 9

shuffling all y to the right and al numbers to the left side gives

18 = 18y

or y = 1

====

which used in A': x = 9 - y gives

x = 8

====

Hence the sought number "xy" = 81

(Control: x + y = 9 and 81 - 63 = 18 or "yx" as required ;-)

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