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

$13.26$

$14.84$

$12.75$

$15.18$

✅ Correct Option: 1

Let their September incomes be $8k$ , $6k$ , and $5k$ respectively, where $k$ is some positive number.

Each person pays a percentage of their income toward rent:

Kamal pays: $15\%$ of $8k = \tfrac{15}{100} \times 8k = 1.2k$

Amal pays: $12\%$ of $6k = \tfrac{12}{100} \times 6k = 0.72k$

Vimal pays: $18\%$ of $5k = \tfrac{18}{100} \times 5k = 0.9k$

Total house rent = $1.2k + 0.72k + 0.9k = 2.82k$

The house rent stays the same in October, so this $2.82k$ amount remains constant.

Person	Sept	% Increase	Multiplier	October
Kamal	$8k	10%	1.10	$8.8k
Amal	$6k	12%	1.12	$6.72k
Vimal	$5k	15%	1.15	$5.75k
Total				$21.27k

Now we have:

House rent (unchanged): $2.82k$
Total income in October: $21.27k$

Percentage formula: $\tfrac{\text{Part}}{\text{Whole}} \times 100$

Percentage = $\tfrac{2.82k}{21.27k} \times 100$

Percentage = $\tfrac{2.82}{21.27} \times 100$

$\tfrac{2.82}{21.27} = 0.1326...$

Therefore: $0.1326 \times 100 = 13.26\%$

This makes intuitive sense: their incomes all increased, but the rent stayed the same, so rent should represent a smaller percentage of their total income compared to September.

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