Question

Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is

• A. 2 : 3
• B. 5 : 4
• C. 4 : 5
• D. 3 : 2

Answer 1

Answer:

C. 4 : 5

• Assume the Third Number: For convenience in percentage calculations, it's often easiest to assume the 'third number' as 100. This makes percentage calculations straightforward as 'X% of 100' is simply X.

• Calculate the First Number: The first number is 20% more than the third number.
  First Number = Third Number + 20% of Third Number
  First Number = 100 + (20/100) * 100 = 100 + 20 = 120.

• Calculate the Second Number: The second number is 50% more than the third number.
  Second Number = Third Number + 50% of Third Number
  Second Number = 100 + (50/100) * 100 = 100 + 50 = 150.

• Determine the Ratio: Now, we need the ratio of the first number to the second number.
  Ratio = First Number : Second Number
  Ratio = 120 : 150.

• Simplify the Ratio: To simplify a ratio, find the greatest common divisor (GCD) of both numbers and divide each number by the GCD. The GCD of 120 and 150 is 30.
  Divide both by 30: (120/30) : (150/30) = 4 : 5.

Alternative Approach (Using Fractions)

• A 20% increase means multiplying by 1 + 20/100 = 1 + 1/5 = 6/5.

• A 50% increase means multiplying by 1 + 50/100 = 1 + 1/2 = 3/2.

• Let the third number be 'x'.
  First number = x * (6/5)
  Second number = x * (3/2)

• Ratio = (x * 6/5) : (x * 3/2)

• Cancel out 'x': (6/5) : (3/2)

• To clear the denominators, multiply both sides by the LCM of 5 and 2 (which is 10):
  (6/5) * 10 : (3/2) * 10
  12 : 15

• Simplify by dividing by 3: 4 : 5.