Question

In a two digits number the unit digits is twice the ten's digit . if 27 is added to the number the digits interchange their places find the number​

Answer 1

$\large\bf\underline{Given:-}$

• unit digit is twice the ten's digit .
• if 27 is added to the number the digits interchange their places.

$\large\bf\underline {To \: find:-}$

• The number.

$\huge\bf\underline{Solution:-}$

Let ten's place digit be x.

then unit's place digit is 2x

• Number = 10x + 2x = 12x

$\bf \: \underbrace{According \: to \: question}$

If 27 is added to the number the digits interchange their places.

$\longmapsto \rm \: 12x + 27 = 21x \\ \\ \longmapsto \rm \:27 = 21x - 12x \\ \\ \longmapsto \rm \: 27 = 9x \\ \\ \longmapsto \rm \: x = \cancel \frac{27}{9} \\ \\ \longmapsto \bf \: x = 3$

ten's place digit x = 3

units place digit 2x = 2×3 = 6

So the Number = 30 + 6

★ The number = 36

Answer 2

Answer:

Given:

• In a two digits number the unit digits is twice the ten's digit. If find the number, If 27 is added to the number the digits interchange their places.

Find:

• Find the number.

Calculations:

• Let x be the number, 2x be be units place and y be tens place.

⇒ ${\bold{\underline{\boxed{\red{\bold{ x = 10x + 2x = 12x}}}}}}$

• Now, If the number if 27 is added to the number the digits interchange their places.

⇒ $\bold{12x + 27 = 21x}$

⇒ $\bold{27 = 21x - 12x}$

⇒ $\bold{27 = 9x}$

⇒ $\bold{y = \cancel{\dfrac{27}{9}}}$

⇒ ${\bold{\underline{\boxed{\red{\bold{y = 3 }}}}}}$

Therefore, 3 is the ten's place digit.

Finding the number:

⇒ $\bold{2x = 2 \times 3 = 6}$

⇒ $\bold{x = 30 + 6}$

⇒ ${\bold{\underline{\boxed{\red{\bold{x = 36 }}}}}}$

Therefore, 36 is the required number.