Question

The ratio of the number of girls to the number of boys in a school of 720 students is 3:5. If 18 new boys are admitted, how many new girls may be admitted so that the ratio changes to 2:3?

• A. 21
• B. 42
• C. 84
• D. 168

Hint:

Divide the total (720) by the sum of ratio parts (8) to quickly find the actual numbers.

Answer 1

The Correct Option is B

Step 1: Initial Calculation
Total parts = $3+5 = 8$. Value per part = $720/8 = 90$.
Girls = $3 \times 90 = 270$. Boys = $5 \times 90 = 450$.

Step 2: Analysis
New boys = $450 + 18 = 468$. Let new girls admitted be $G$.
New total girls = $270 + G$.

Step 3: Reasoning
New ratio: $(270 + G) / 468 = 2/3$.
$3(270 + G) = 2(468)$
$810 + 3G = 936$
$3G = 126 \Rightarrow G = 42$.

Step 4: Conclusion
42 new girls must be admitted. Final Answer: (B)