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
Question:
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
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
Options
Answer: 13.26
Explanation:
Step 1: Represent incomes Let September incomes of Kamal, Amal, Vimal be: K = 8x, A = 6x, V = 5x Step 2: Calculate September rent shares Kamal pays 15% of 8x → 0.15 × 8x = 1.2x Amal pays 12% of 6x → 0.12 × 6x = 0.72x Vimal pays 18% of 5x → 0.18 × 5x = 0.9x Total house rent = 1.2x + 0.72x + 0.9x = 2.82x Step 3: October incomes Kamal: 10% increase → 8x × 1.10 = 8.8x Amal: 12% increase → 6x × 1.12 = 6.72x Vimal: 15% increase → 5x × 1.15 = 5.75x Total October income = 8.8 + 6.72 + 5.75 = 21.27x Step 4: Percentage of total income for rent Rent unchanged = 2.82x Percentage = (2.82x / 21.27x) × 100 ≈ 13.26%
Explanation:
Step 1: Represent incomes Let September incomes of Kamal, Amal, Vimal be: K = 8x, A = 6x, V = 5x Step 2: Calculate September rent shares Kamal pays 15% of 8x → 0.15 × 8x = 1.2x Amal pays 12% of 6x → 0.12 × 6x = 0.72x Vimal pays 18% of 5x → 0.18 × 5x = 0.9x Total house rent = 1.2x + 0.72x + 0.9x = 2.82x Step 3: October incomes Kamal: 10% increase → 8x × 1.10 = 8.8x Amal: 12% increase → 6x × 1.12 = 6.72x Vimal: 15% increase → 5x × 1.15 = 5.75x Total October income = 8.8 + 6.72 + 5.75 = 21.27x Step 4: Percentage of total income for rent Rent unchanged = 2.82x Percentage = (2.82x / 21.27x) × 100 ≈ 13.26%
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