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.

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Answer 1

Heya

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Let the two digit number be xy

ACCORDING TO THE QUESTION

y = 2x

10x + y + 27 = 10y + x

=>

9x - 9y = -27

=>

y - x = 3

put value of y = 2x in above equation

=>

2x - x = 3

=>

x = 3 And y = 6

So, the two digit number is 36

Answer 2

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.

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To Find :

• The number

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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