Averages , Ratio and Proportion Question 4 - CAT 2024
In September, the incomes of Kamal, Amal and Vimal are in the ratio 8 ∶ 6 ∶ 5. They rent a house together, and Kamal pays 15%, Amal pays 12% and Vimal pays 18% of their respective incomes to cover the total house rent in that month. In October, the house rent remains unchanged while their incomes increase by 10%, 12% and 15%, respectively. In October, the percentage of their total income that will be paid as house rent, is nearest to:
Step-by-Step Explanation
Assume a convenient baseline scale for their September incomes:
Iₖ = 80, Iₐ = 60, Iᵥ = 50
- Calculate the total house rent:
- Kamal's rent share = 15% of 80 = 12
- Amal's rent share = 12% of 60 = 7.2
- Vimal's rent share = 18% of 50 = 9
Total Rent Paid = 12 + 7.2 + 9 = 28.2
- Calculate the updated October incomes:
- Kamal's new income = 80 × 1.10 = 88
- Amal's new income = 60 × 1.12 = 67.2
- Vimal's new income = 50 × 1.15 = 57.5
Total October Income Pool = 88 + 67.2 + 57.5 = 212.7
- Determine the new rent percentage:
Since the absolute total rent remains unchanged at 28.2:
Percentage = 28.2/212.7 × 100%
≈ 13.258%
≈ 13.26%
Correct Option: B
💡 FundaMakers Tip:
Scaling ratios up by a factor of 10 or 100 (e.g., 80, 60, 50) makes percentage operations straightforward. Keeping track of the fixed absolute total rent (28.2) and dividing it by the newly updated income base (212.7) provides the final percentage quickly.