CAT 2024 Slot 1 · Quant · Question 6

CAT 2024 Slot 1 previous year question on Percentage, with the answer and a step-by-step solution.

PercentageArithmeticMultiple choiceMedium

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

A
14.84
B
12.75
C
13.26
D
15.18

Pick an option, then check.

Answer & solution

Answer: Option C

Take the September incomes as 8x, 6x and 5x.

The rent is the sum of their three contributions: 0.15\left( 8x \right)+0.12\left( 6x \right)+0.18\left( 5x \right).

That is 1.2x+0.72x+0.9x=2.82x, and the rent stays at this figure in October.

The October incomes are 8x\times 1.10=8.8x, 6x\times 1.12=6.72x and 5x\times 1.15=5.75x.

Their October total is 8.8x+6.72x+5.75x=21.27x.

The required percentage is \frac{2.82x}{21.27x}\times 100.

The x cancels, leaving \frac{282}{21.27}=13.258\ldots

The nearest option is 13.26.

Shortcut. The rent is a fixed amount, so only the denominator changes. Compute the rent once as 2.82x, grow the incomes, and divide — the individual percentages are never needed again.

CAT 2024 Slot 1 · Quant · Question 6

More Percentage questions