Question

the sum of the digits of a two digit no is 12.the number obtained by interchanging the two digit exceeds the given numbers by 18.find the no

Answer 1

$\huge{\sf{\boxed{\boxed{Answer:57}}}}$

Given that :-

The sum of the digits of a two digit number is 12.

The number obtained by interchanging the two digits exceeds the given number by 18.

To find :-

The number.

Solution

Let the digit in the tens place be x

Let the digit in the tens place be y

Original number = 10x + y

As per 1st condition:-

The sum of the digits of a two digit number is 12.

Representing it mathematically,

=> x + y = 12 ----> 1

As per 2nd condition:-

The number obtained by interchanging the two digits exceeds the given number by 18

Reversed number = 10y + x

Representing the second condition mathematically.

=> 10y + x = 10x + y + 18

=> 10x + y + 18 =10y + x

=> 10x - x + 18 = 10y - y

=> 9x + 18 = 9y

=> 9x - 9y = - 18

=> 9 ( x - y) = - 18

=> x - y =

=> x - y = - 2 -----> 2

Solve equations 1 and 2 simultaneously by elimination method.

Add equation 1 to equation 2,

x + y = 12

x - y = - 2

2x = 10

=> x = 5

$\bold{=> x = 5}$

Substitute x = 5 in equation 2,

=> x - y = - 2

=> 5 - y = - 2

=> - y = - 2 - 5

=> - y = - 7

$\bold{=> y = 7}$

$\bold{10×5+7=\:57}$