Question

The numbers of students studying Physics, Chemistry and Zoology in a college were in the ratio 4 : 3 : 5 respectively. If the number in these three disciplines increased by 50%, 25% and 10% respectively in the next year, then what was the new respective ratio?

• A. 24 : 15 : 22
• B. 18 : 11 : 13
• C. 24 : 13 : 17
• D. Cannot be determined

Answer 1

The Correct Option is A

Let the initial number of students studying Physics, Chemistry, and Zoology be 4x, 3x, and 5x respectively. We need to calculate the new numbers after the specified percentage increases and find the new ratio.

1. Calculate the new number of Physics students: Initial number = 4x. Increase = 50%. New number = 4x + 0.50(4x) = 4x + 2x = 6x.
2. Calculate the new number of Chemistry students: Initial number = 3x. Increase = 25%. New number = 3x + 0.25(3x) = 3x + 0.75x = 3.75x.
3. Calculate the new number of Zoology students: Initial number = 5x. Increase = 10%. New number = 5x + 0.10(5x) = 5x + 0.5x = 5.5x.
4. Express the new numbers as a ratio: 6x : 3.75x : 5.5x.
5. Simplify the ratio by dividing all terms by the smallest value, 3.75:
   
   Physics students: \(\frac{6x}{3.75}=1.6\).
   Chemistry students: \(\frac{3.75x}{3.75}=1\).
   Zoology students: \(\frac{5.5x}{3.75}\approx1.4667\).
6. For clarity, re-express this ratio in whole numbers by multiplying each part by 15 (LCM of 1.6, 1, and 1.4667):
   
   Physics: 1.6*15 = 24.
   Chemistry: 1*15 = 15.
   Zoology: 1.4667*15 ≈ 22.

Thus, the new respective ratio is: 24 : 15 : 22.