Question

A number consists of two digits whose sum is 9,when 27 is added to this number,the digits interchange their places. The number is…………

Solve this is question using one variable​

Answer 1

Answer :

$\large\boxed{\bf{\star\:\:The\:Required\:Number\:is\:36\:.\:\:\star}}$

Explanation :

Given :–

• Sum of a two digit number is 9 .

• Number obtained by reversing the digits will be 27 more than the Original Number.

To Find :–

• The Original Number.

Solution :–

Let the First digit of the Original Number be x and the Second digit be y .

→ According to the First Condition :-

⇒ x + y = 9

⇒ x = 9 - y  ------------(1)

→ According to the Second Condition :-

⇒ 10y + x = 27 + (10x + y)

⇒ 10y + x = 27 + 10x + y

⇒ 10y - y + x - 10x = 27

⇒ 9y - 9x =27

⇒ -9(x - y) = 27

⇒ x - y = 27 ÷ (-9)

⇒ x - y = (-3)  -----------(2)

Putting 'x' from Equation (1) in Equation(2) :-

⇒ (9 - y) - y = (-3)

⇒ 9 - y - y = (-3)

⇒ 9 - 2y = (-3)

⇒ 9 + 3 = 2y

⇒ 2y = 12

⇒ y = 12 ÷ 2

⇒ y = 6

Now , putting value of 'y' in Equation(1) :-

⇒ x = 9 - 6

⇒ x = 3

Now , we have :

➨ First Digit ( x ) = 3

➨ Second Digit ( y ) = 6

→ The number will be 10(3) + 6 = 30 + 6 = 36 .

∴ The required number is 36 .