Question

in a two digit number digit in units place is twice the digit in tens place if 27 is added to it, digit are reversed. find the number

Answer 1

Hi,

Here it's given that
There is a 2 digits number

Let the 2nd digit be x
So 1 st digit would be y = 2x...... Given in the question

So,

It is also given that when 27 is added it is reversed

Therefore
10y + x + 27 = 10 x + y
9y - 9x + 27 = 0
9( y - x) = - 27
9( 2x - x) = - 27
-9x = - 27
x = 3

Therefore we got the 2nd digit = 3
Now first digit = 2x = 2(3) = 6

Therefore the number = 36 or 63

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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.

___________________________

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