Question

The ratio between two numbers is 6 : 5. If 30% of the first number is 12, what would be 60% of the second number?

• A. 12
• B. 15
• C. 18
• D. 20
• E. 23

Answer 1

The Correct Option is D

Step 1: Understand the problem.
The ratio between two numbers is given as 6:5. We are also told that 30% of the first number is 12. We need to find what 60% of the second number is.

Step 2: Let the two numbers be \( x \) and \( y \).
From the given ratio, we have: \[ \frac{x}{y} = \frac{6}{5} \] This implies: \[ x = \frac{6}{5}y \]

Step 3: Use the information about the first number.
We are told that 30% of the first number \( x \) is 12. This gives the equation: \[ 0.30x = 12 \] Solving for \( x \): \[ x = \frac{12}{0.30} = 40 \]

Step 4: Find the second number \( y \).
Since \( x = \frac{6}{5}y \), we can substitute \( x = 40 \) into this equation: \[ 40 = \frac{6}{5}y \] Solving for \( y \): \[ y = \frac{40 \times 5}{6} = \frac{200}{6} = \frac{100}{3} \approx 33.33 \]

Step 5: Find 60% of the second number \( y \).
Now, we need to calculate 60% of \( y \): \[ 0.60y = 0.60 \times \frac{100}{3} = \frac{60}{3} = 20 \]

Step 6: Conclusion.
60% of the second number is 20.

Final Answer:
The correct option is (D): 20.