Question

The sum of the digit of a two digit number is 12. The number obtained by the interchanging the digits exceeds the given number by 18. Find the number.​

Answer 1

let unit digit = x, tens digit = y, so number = (10y + x)

now, x + y = 12 ---------------(1) equation

because original digit is (10y + x) and interchanged digit is (10x + y) that exceeds 18 from (10y + x)

i.e the difference of original digit and exchanged digit =18

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

10x + y - 10y - x = 18

9x - 9y = 18 or x - y = 2----------------(2) equation

from equation (1)&(2)

x = 7, y = 5

so number (10y + x) = 10×5+7 = 57

Answer 2

ANSWER

Let the tens digit of the required number be x and the units digit be y. Then,

x+y=12 .........(1)

Required Number = (10x+y).

Number obtained on reversing the digits = (10y+x).

Therefore,

(10y+x)−(10x+y)=18

9y−9x=18

y−x=2 ..........(2)

On adding (1) and (2), we get,

2y=14⟹y=7

Therefore,

x=5

Hence, the required number is 57.