Question

6. I am thinking of a two-digit number. If I write 3 to the left of my number, and double this three digit number, the result is 27 times my original number. What is my original number? ​

Answer 1

Answer:

What is my original number? ​

24

Step-by-step explanation:

• Let the number be ab

• a is in 10's place and b is in units place so actual value of two digits a and b as above = 10a + b

• If we add 3 to the left of ab, the number consists of digits 3ab
  
• 3 is in the 100's place now so the actual value of this 3 digit number = 300 + 10a + b

• We ae given that doubling the new 3-digit number will give us a number that is 27 times the original number

• This means
  2(300 + 10a + b) = 27(10a + b)
  => 600 + 2(10a + b) = 27(10a + b)

• Switch sides:
  27(10a + b) = 600 + 2(10a + b)

• Subtract 2(10+b) from both sides:
  27(10a + b) - 2(10a + b) = 600

• Simplify:
  25(10a + b) = 600   (27 - 2  = 25 and 10a+b is common)

• Divide by 25:
  10a + b = 600/25
  10a + b = 24

• But 10a + b is the value of our original number

*** Hence a= 2 and b = 4 and the number is 24 ***