Question

Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?

• A. 2 : 3
• B. 6 : 7
• C. 6 : 8
• D. None of these

Hint:

When dealing with percentage increases in ratios, always apply the percentage to the original value and simplify the ratio at the end.

Answer 1

The Correct Option is C

Step 1: Take the original seats for Mathematics, Physics and Biology in the ratio \( 5x : 7x : 8x \).
Step 2: Apply the given percentage increases: Mathematics becomes \( 5x \times 1.40 = 7x \), Physics becomes \( 7x \times 1.50 = 10.5x \), and Biology becomes \( 8x \times 1.75 = 14x \).
Step 3: Writing these as a ratio, \( 7x : 10.5x : 14x \), and multiplying through by \( 2 \) to clear the decimal gives \( 14x : 21x : 28x \), which reduces to \( 2 : 3 : 4 \), equivalent to \( 4 : 6 : 8 \).
So the increased seats are in the ratio \( 4 : 6 : 8 \), matching the pairing: \[ \boxed{6 : 8} \]

Answer 2

A different way to reach the same result is to convert each percentage increase into a fraction and multiply it directly into the original ratio terms, without introducing decimals at any stage.

1. 2 : 3: Mathematics increases by \( 40\% \), so its new share is \( \frac{7}{5} \) of \( 5 \), giving \( 7 \). Physics increases by \( 50\% \), so its new share is \( \frac{3}{2} \) of \( 7 \), giving \( \frac{21}{2} \). The ratio of these two, \( 7 : \frac{21}{2} \), simplifies to \( 2 : 3 \), which is a genuine part of the final answer but only covers two of the three subjects.
2. 6 : 7: No combination of the fractional increases applied to \( 5, 7, 8 \) produces a \( 6 : 7 \) pairing between any two subjects, so this option can be ruled out directly.
3. 6 : 8: Biology increases by \( 75\% \), so its new share is \( \frac{7}{4} \) of \( 8 \), giving \( 14 \). Comparing this with Physics's new share of \( \frac{21}{2} \), the ratio \( \frac{21}{2} : 14 \) clears to \( 21 : 28 \), which reduces to \( 3 : 4 \), the same as \( 6 : 8 \).
4. None of these: Not needed, since the fractional method reproduces a valid pairing that matches option (C).

Using fractions instead of decimal multipliers leads to the same final increased ratio, \( 2 : 3 : 4 \), confirming the \( 6 : 8 \) pairing.

Therefore, the correct answer is 6 : 8.