In one month, the earnings of Ravi, Sunil and Manoj are in the ratio 8:6:5. They contribute 15%, 12% and 18% of their respective earnings towards the total house rent. In the following month, the rent remains unchanged, while their earnings increase by 10%, 12% and 15%, respectively. What percentage of their combined earnings is spent on rent in the following month? Give the answer to the nearest 0.1%.
Answer and solution
Correct answer: C
Solution
Answer: C — 13.3%
1. Use earnings 8k,6k,5k. Rent=0.15(8k)+0.12(6k)+0.18(5k)=2.82k.
2. Next-month incomes are 8.8k,6.72k,5.75k. Their total is 21.27k.
3. The rent is unchanged, so its new share is (2.82/21.27)×100=13.2581…%.
4. Rounded to the nearest 0.1%, the answer is 13.3%, option C. Do not average the three individual contribution percentages.
Why this method works:
Percentages must be weighted by each person’s earnings. With incomes₹800,₹600,₹500, contributions are₹120,₹72,₹90. The same₹282 rent is then compared with the new total income, not the old₹1,900 total.
Independent check and common trap:
New incomes₹880,₹672,₹575 total₹2,127. The ratio 282/2127×100 is 13.2581…%, which rounds upward to 13.3% at one decimal. OptionB 13.2% is truncation rather than rounding; the original rent share 14.84% uses the wrong month.
Apply: Choose earnings 800,600,500. Rent=282 and new total=2127. Compute 282/2127×100≈13.258%, then round once to 13.3%.
Check: New incomes₹880,₹672,₹575 total₹2,127. The ratio 282/2127×100 is 13.2581…%, which rounds upward to 13.3% at one decimal. OptionB 13.2% is truncation rather than rounding; the original rent share 14.84% uses the wrong month.
1. Use earnings 8k,6k,5k. Rent=0.15(8k)+0.12(6k)+0.18(5k)=2.82k.
2. Next-month incomes are 8.8k,6.72k,5.75k. Their total is 21.27k.
3. The rent is unchanged, so its new share is (2.82/21.27)×100=13.2581…%.
4. Rounded to the nearest 0.1%, the answer is 13.3%, option C. Do not average the three individual contribution percentages.
Why this method works:
Percentages must be weighted by each person’s earnings. With incomes₹800,₹600,₹500, contributions are₹120,₹72,₹90. The same₹282 rent is then compared with the new total income, not the old₹1,900 total.
Independent check and common trap:
New incomes₹880,₹672,₹575 total₹2,127. The ratio 282/2127×100 is 13.2581…%, which rounds upward to 13.3% at one decimal. OptionB 13.2% is truncation rather than rounding; the original rent share 14.84% uses the wrong month.
G Strategy shortcut
Spot: Percentages.Apply: Choose earnings 800,600,500. Rent=282 and new total=2127. Compute 282/2127×100≈13.258%, then round once to 13.3%.
Check: New incomes₹880,₹672,₹575 total₹2,127. The ratio 282/2127×100 is 13.2581…%, which rounds upward to 13.3% at one decimal. OptionB 13.2% is truncation rather than rounding; the original rent share 14.84% uses the wrong month.
G Strategy: Spot: Percentages. Apply: Choose earnings 800,600,500. Rent=282 and new total=2127. Compute 282/2127×100≈13.258%, then round once to 13.3%. Check: New incomes₹880,₹672,₹575 total₹2,127. The ratio 282/2127×100 is 13.2581…%, which rounds upward to 13.3% at one decimal. OptionB 13.2% is truncation rather than rounding; the original rent share 14.84% uses the wrong month.