Question

In a two digit number, digit in units place is twice the digit in tens place. If 27 is added to it,
digits are reversed. Find the number.

Answer 1

Given :

In a two digit number. Digit in the units place is twice the digit in tens place. If 27 is added to it, the digits are reversed.

___________________________

To Find :

• The number

___________________________

Solution :

Let the digit in the ten's place be → x

Digit in one's place → 2x

Original number → 10 (x) + 1 (2x)

→ 10x + 2x

→ 12x

After reversing the digits,

Unit's digit → x

Ten's place → 2x

Number obtained → 10 (2x) + 1 (x)

→ 20x + x

→ 21x

According to the question, when 27 is added to the original number the digits get reversed. So we will solve this equation to find the original number ⇒ 12x + 27 = 21x

Let's solve your equation step-by-step

12x + 27 = 21x

Step 1 :

Subtract 21x from both sides of the equation.

⇒ 12x + 27 - 21x = 21x - 21x

⇒ -9x + 27 = 0

Step 2 :

Subtract 27 from both sides of the equation.

⇒ -9x + 27 - 27 = 0 - 27

⇒ -9x = -27

Step 3 :

Cancel out the negative sign from both sides.

⇒ -9x = -27

⇒ 9x = 27

Step 4 :

Divide 9 from both sides of the equation.

⇒ 9x ÷ 9 = 27 ÷ 9

⇒ x = 3

The unit's digit ⇒ 2x = 2(3) = 6

The ten's digit ⇒ x = 3

∴ The number is 36