Question

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

Answer 1

$\bf{\huge{\underline{\boxed{\sf{\green{Answer:}}}}}}$

$\bf{\underline{\underline{\sf{\blue{Given:}}}}}$

• 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

$\bf{\underline{\underline{\sf{\blue{To\:find:}}}}}$

• The number.

$\bf{\underline{\underline{\sf{\blue{Solution:}}}}}$

Let the digit in the tens place be x

Let the digit in the tens place be y

Original number = 10x + y

$\bf{\underline{\underline{\sf{\blue{As\:per\:first\:condition:}}}}}$

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

Representing it mathematically,

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

$\bf{\underline{\underline{\sf{\blue{As\:per\:second\:condition:}}}}}$

• 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 = $\large\frac{-18}{9}$

=> 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 = $\large\frac{10}{2}$

=> x = 5

Substitute x = 5 in equation 2,

=> x - y = - 2

=> 5 - y = - 2

=> - y = - 2 - 5

=> - y = - 7

=> y = 7

$\bf{\large{\underline{\boxed{\sf{\purple{Digit\:in\:the\:units\:place\:=\:x\:=\:5}}}}}}$

$\bf{\large{\underline{\boxed{\sf{\purple{Digit\:in\:the\:tens\:place\:=\:y\:=\:7}}}}}}$

$\bf{\large{\underline{\boxed{\sf{\purple{Original\:number \:=\:10x\:+\:y\:=\:10\times\:5\:+7\:=\:50\:+7\:=\:57 }}}}}}$

Answer 2

Let x and y be the two digits of the number

Therefore, two-digit number is

= 10x + y

Reversed number = 10y + x

As per the question :

x + y = 12

y = 12 – x -----------1

Also given:

10y + x - 10x – y = 18

9y – 9x = 18

y – x = 2 -------------2

Substituting the value of y from eqn 1 in eqn 2

12 – x – x = 2

12 – 2x = 2

2x = 10

x = 5

Therefore, y = 12 – x = 12 – 5 = 7

Therefore, the two-digit number is 10x + y = (10×5) + 7 = 57