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CAT 2024 Slot 1 — QA Question 6

PercentageEasy

 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

Answer & solution

  • A

    12.75

  • B

    14.84

  • C

    15.18

  • 13.26

Solution

Medium

Pick convenient incomes in the ratio 8:6:58:6:5. Compute September's rent (a fixed amount), then grow each income for October and express that same rent as a percentage of the new total income.

1

Assign incomes and find the rent. Let Kamal, Amal, Vimal earn 800,600,500800,600,500 in September. Rent =15%+12%+18%=15\%+12\%+18\% of their incomes.

Rent=0.15(800)+0.12(600)+0.18(500)⇒ Rent=120+72+90(each share)⇒ Rent=282\begin{aligned} &\text{Rent}=0.15(800)+0.12(600)+0.18(500)\\ &\Rightarrow\ \text{Rent}=120+72+90 \quad\text{(each share)}\\ &\Rightarrow\ \text{Rent}=282 \end{aligned}
2

Grow incomes for October. Increase by 10%,12%,15%10\%,12\%,15\% respectively.

Kamal=800×1.10=880⇒ Amal=600×1.12=672⇒ Vimal=500×1.15=575⇒ Total=880+672+575=2127\begin{aligned} &\text{Kamal}=800\times1.10=880\\ &\Rightarrow\ \text{Amal}=600\times1.12=672\\ &\Rightarrow\ \text{Vimal}=500\times1.15=575\\ &\Rightarrow\ \text{Total}=880+672+575=2127 \end{aligned}
3

Rent as a percentage of October income. Rent is unchanged at 282282 (step 1) against the new total (step 2).

Percent=2822127×100⇒ Percent≈13.258(divide)⇒ Percent≈13.26\begin{aligned} &\text{Percent}=\dfrac{282}{2127}\times100\\ &\Rightarrow\ \text{Percent}\approx 13.258 \quad\text{(divide)}\\ &\Rightarrow\ \text{Percent}\approx 13.26 \end{aligned}
≈13.26%\approx 13.26\%
CAT 2024 Slot 1 QA Q6: In September, the incomes of Kamal, Amal and Vimal are in the ratio 8 ∶ 6 ∶ 5. They rent a house together, — Solution | TheCATExam