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
- 14.84
- 13.26
- 15.18
- 12.75
The Correct Option is B
Solution and Explanation
Let Kamal's income be $8x$, Amal's income be $6x$, and Vimal's income be $5x$.
- The total income in September is $8x + 6x + 5x = 19x$.
In September, Kamal pays \(15\%\), Amal pays \(12\%\), and Vimal pays \(18\%\) of their respective incomes.
- Kamal's contribution: $15\% \times 8x = 0.15 \times 8x = 1.2x$.
- Amal's contribution: $12\% \times 6x = 0.12 \times 6x = 0.72x$.
- Vimal's contribution: $18\% \times 5x = 0.18 \times 5x = 0.9x$.
The total rent in September is:
$1.2x + 0.72x + 0.9x = 2.82x$.
In October, their incomes increase by \(10\%\), \(12\%\), and \(15\%\), respectively.
- Kamal's new income = $8x \times 1.10 = 8.8x$.
- Amal's new income = $6x \times 1.12 = 6.72x$.
- Vimal's new income = $5x \times 1.15 = 5.75x$.
The total income in October is:
$8.8x + 6.72x + 5.75x = 21.27x$.
Now, the total percentage of their total income that will be paid as rent is:
$\frac{2.82x}{21.27x} \times 100 = 13.26\%$.
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