Question

sum of the digits of a two number is 9 when we interchange the digits it is found that the resulting new number is greater than the original number by 27 what is the 2 digit number

Answer 1

Let the unit digit be y and tens digit be x

Number formed = 10x + y

Reverse number = 10y + x

x + y = 9 (Given)…………………………eq1

10y + x = 10x + y + 27…………………….eq2

9y - 9x = 27

y - x = 3……………………………………..eq3

Solving eq1 and eq3 ,we get

x = 3 and y = 6

Original Number = 36 Reversed Number = 63

You can crosscheck the answer by putting up the values obtained either in eq1 or eq2 or eq 3

Answer 2

Let unit digit be Y and Tens digit be X

According to question-
X+Y = 9--------(1)

(10Y +X) - (10X+Y) = 27-----(2)
10Y + X -10X -Y = 27
9(Y-X) = 27
Y-X = 3

X + Y = 9
X + Y +Y -X = 9+3
Y = 12/2
Y = 6

then , X = 3

Number is 36