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.
Answers
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