Question

the sum of digits of two digit number is 12 the number obtained by interchanging its digit exceeds the given number by 18 . find the number ​

Answer 1

$\mathfrak{\huge{Solution:-}}$


Let the digit in the number is xy.

So,

Number = 10x + y.

Given,

Sum of the digits of a two - digit number = 12

x + y = 121 $\: \: \: \: \: \: \: \: \: \sf........(1)$


Again,

✏ 10y + x = 10x+ y +18

✏ 10y + x - 10x - y = 18

✏ 9y -9x = 18

✏ y - x = 2 $\: \: \: \: \: \: \: \: \: \: \sf........(2)$


Solving equation 1 and 2, we get

x = 5, y = 7

So the number is $\boxed{\boxed{\sf 57}}$

Answer 2

Answer:

let the number in the tens place be x

let the number in the ones place be y

original number = 10x +y

interchanged number = 10y +x

ATQ

x+y = 12

y = 12 - x

10x + y +18 = 10y + x

but y = 12 - x

10x + 12 -x +18 = 10( 12 - x ) +x

9x + 30 = 120 - 10x +x

9x + 30 = 120 - 9x

18x = 90

x = 5

therefore y = 12 - 5

                y = 7

original number = 57

and interchanged number is 75