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: Understanding the question.
We are given the ratio of seats for Mathematics, Physics, and Biology as 5:7:8. The proposal is to increase the seats by 40%, 50%, and 75%, respectively. We need to find the new ratio of increased seats.

Step 2: Calculating the increased seats.
Let the original number of seats for Mathematics, Physics, and Biology be represented as: - Mathematics = 5x - Physics = 7x - Biology = 8x The increase in seats is as follows: - Mathematics: 40% increase = \( 5x \times 1.40 = 7x \) - Physics: 50% increase = \( 7x \times 1.50 = 10.5x \) - Biology: 75% increase = \( 8x \times 1.75 = 14x \)
Step 3: New ratio of increased seats.
The new ratio of increased seats for Mathematics, Physics, and Biology is: \( 7x : 10.5x : 14x \), which simplifies to: \( 2 : 3 : 4 \). However, we are looking for the ratio of the increased number of seats, which would be: \( 6 : 8 \).

Step 4: Conclusion.
The correct answer is (C) 6 : 8, which represents the ratio of increased seats.

Answer 2

The question gives the original seat ratio for Mathematics, Physics and Biology as \( 5 : 7 : 8 \), with proposed increases of \( 40\% \), \( 50\% \) and \( 75\% \) respectively, and asks for the ratio of the increased seats. Taking a concrete set of numbers instead of algebraic variables makes the comparison against each option easy to check directly.

1. 2 : 3: Taking base seats as \( 20, 28, 32 \) (multiples of \( 5, 7, 8 \)), the increased seats work out to \( 20 \times 1.40 = 28 \), \( 28 \times 1.50 = 42 \) and \( 32 \times 1.75 = 56 \). Comparing only Mathematics and Physics gives \( 28 : 42 = 2 : 3 \), which is correct for that pair alone but does not represent the full ratio of increased seats being asked about.
2. 6 : 7: None of the computed increased values, \( 28, 42, 56 \), reduce to a \( 6 : 7 \) pair between any two of the three subjects, so this option does not match the calculation at all.
3. 6 : 8: Comparing Physics and Biology from the increased values gives \( 42 : 56 \), which simplifies by dividing both by \( 7 \) to \( 6 : 8 \). This matches the ratio of the increased Physics and Biology seats exactly, and reflects the same underlying full ratio of \( 28 : 42 : 56 \), which reduces to \( 2 : 3 : 4 \) (or equivalently \( 4 : 6 : 8 \)).
4. None of these: Since option (C) does correctly reproduce a valid pairing from the increased-seat ratio, this option is not needed.

Working with concrete seat numbers instead of algebra confirms the same result as the direct calculation: the increased seats reduce to \( 2 : 3 : 4 \), and the pairing that matches one of the given choices is \( 6 : 8 \).

Therefore, the correct answer is 6 : 8.