Let the initial number of oranges in the three baskets be 3k, 4k, and 5k respectively, for some constant k. The new ratio of oranges is 5 : 4 : 3. Let the new number of oranges be 5m, 4m, and 3m for some constant m. The problem implies that the number of oranges in the third basket remains unchanged. So, the original number in the third basket (5k) is equal to the new number in the third basket (3m). 5k = 3m, which means m = 5k/3. The new number of oranges in the three baskets are: Basket 1: 5m = 5 (5k/3) = 25k/3. Basket 2: 4m = 4 (5k/3) = 20k/3. Basket 3: 3m = 3 (5k/3) = 5k (matches original). The original numbers were 3k and 4k for the first two baskets. The increase in the number of oranges in the first basket is (25k/3) - 3k = (25k - 9k)/3 = 16k/3. The increase in the number of oranges in the second basket is (20k/3) - 4k = (20k - 12k)/3 = 8k/3. The question asks for the ratio in which the number of oranges in the first two baskets must be increased. This refers to the ratio of the amounts of increase. Ratio of increase in basket 1 to increase in basket 2 = (16k/3) : (8k/3). Dividing both parts of the ratio by k/3, we get 16 : 8, which simplifies to 2 : 1.
The number of oranges in three baskets are in the ratio 3 : 4 : 5. In which ratio the no. of oranges in first two baskets must be increased so that the new ratio becomes 5 : 4 : 3 ?
Asked in GPSC Prelims CSP 1 2023 · Topic: National Income & Gross Domestic Product (Gross Domestic Product (GDP): Concepts and Measures)
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