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.