Question

The sum of the digits of a 2-digit number is 12.The given number exceeds the number obtained by interchanging the digits by 36. Find the given number.​

Answer 1

Given:-

• A number consists of 2 digits. The sum of its digits is 12.
• The number obtained by interchanging the digits is 36 less than the given number.

To find:-

• Find the number ?

Solutions:-

• Let the digit at unit's place be 'y' and the digit at ten's place be 'x'.

Then,

Number = 10x + y

A number consists of 2 digits. The sum of its digits is 12.

=> x + y = 12 .......(i).

The number obtained by interchanging the digits is 36 less than the given number.

Number obtained by reversing the digits = 10y + x

Number obtained by reversing the digits = Original number - 36

=> 10y + x = 10x + y - 36

=> 10y - y + x - 10x = -36

=> 9y - 9x = - 36

=> 9(y - x) = -36

=> y - x = -36/9

=> y - x = -4

=> x - y = 4

=> x = 4 + y .......(ii)

Putting the value of 'x' from equation (ii) in equation (i)

=> x + y = 12

=> 4 + y + y = 12

=> 4 + 2y = 12

=> 2y = 12 - 4

=> 2y = 8

=> y = 8/2

=> y = 4

Putting the value of 'y' in equation (ii)

=> x = 4 + y

=> x = 4 + 4

=> x = 8

Now,

Number => 10x + y

=> 10(8) + 4

=> 80 + 4

=> 84

Hence, the number is 84.

Answer 2

Answer:

$\huge\star{\red{Q}{uestion}}\star\:$

Sum of the digits of a two-digit number is 12. The given number exceeds the number obtained by interchanging the digits by 36. Find the given

number.

$\huge\star{\red {A}{nswer}}\star\:$

$\huge\underline {Let,}$

The tens digit of the required number be x

and the units digit be y

\huge\underline {Then,}

Then,

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

Required number = (10x + y)

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

$\huge\underline {Therefore,}$

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

9y - 9x = 18

x - y = 12 ......... eq. (2)<br>

On adding eq. (1) and eq. (2)

$\huge\underline {We\: get}$

x + y + y - x = 12 +2

2y = 14

y = 2

$\huge\underline {Therefore}$

x = 5

Hence, the required number is 57

$\huge\green { Hope\: this\: helps\: you}$