Question

A two digit number is such that the sum of digits is 6. If 18 is added to the number, its digits are reversed. Then find the number. *​

Answer 1

${\huge{\underline{\boxed{\red{\mathcal{Answer}}}}}}$

Given:

• Sum of digits of a number = 6
• After adding 18 to it, digits get reversed.

To find:

• The number.

Assumption:

• Let the unit digit and tens digit of the number be x and y respectively.

Solution:

The number = 10y + x (y is the tens digit)...

According to question,

x + y = 6 ------------(i)

And,

10y + x + 18 = 10x + y

=> 9x - 9y = 18

=> x - y = 2 -------------(ii)

Adding (i) & (ii),

=> x + y + x - y = 6 + 2

=> 2x = 8

=> x = 4

So,

=> x + y = 6

=> 4 + y = 6

=> y = 2.

So,

The number = 10y + x => 10*2 + 4 => 24.

The number is 24.

HOPE IT HELPS!!!!

Answer 2

       SOLUTION      

Let the number in unit place be 'x' .

Let the number in ten's place be 'y' .

So the two digit number is  10y+x

∵ Given that the sum of digits is 6.

$\implies$

x + y = 6 $\longrightarrow$(1)

∵ Given that the if 18 is added to the number, its digits are reversed.

$\implies$

10y + x + 18 = 10x + y

10x + y - 10 y + x =18

9x - 9y = 18

On dividing throughout by 9,

x - y = 2$\longrightarrow$(2)

Now , Let us solve the two equations to find the value of x and y.

           

              x + y = 6

              x -  y  =  2              

            2x        = 8

∵ 2x = 8

$\sf x = \dfrac{8}{2} =4$    

$\red\bigstar$ Value of x = 4

To find the value of y substitute the value of 'x' in (2)

$\implies$ 4  - y = 2

   - y = 2 - 4

   - y = -2

     y =  2  

$\red\bigstar$ Value of y = 2

Now let us find the two digit number 10y + x , by substituting the values of y and x respectively.

$\boxed{\sf Two \: digit \: number = 10 * 2 + 4 = 20 + 4 =24}$