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Alligation: find the ratio in which two mixtures (or two profit rates) are combined to reach a target

This type of question, asked 3 times: 15 Nov 2020 Tier II, 3 Feb 2022 Tier II, 18 Jan 2025 Tier II. All 3 questions below, oldest first.

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  1. Question 1

    15 Nov 2020 Tier II

    62
    A and B are solutions of acid and water. The ratios of water and acid in A and B are 4:54 : 5 and 1:21 : 2, respectively. If xx litres of A is mixed with yy litres of B, then the ratio of water and acid in the mixture becomes 8:138 : 13. What is x:yx : y?

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  2. Question 2

    3 Feb 2022 Tier II

    33
    A trader bought 640 kg of rice. He sold a part of the rice at 20% profit and the rest at 5% loss. He earned a profit of 15% in the entire transaction. What is the ratio of the quantity of rice that he sold at a loss of 5% to that of the quantity that he sold at a profit of 20%?

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  3. Question 3

    18 Jan 2025 Tier II

    25
    Vessel A contains milk and water in the ratio 4:54 : 5. Vessel B contains milk and water in the ratio 2:12 : 1. If x litres mixture of A is mixed with y litres mixture of B, then the ratio of milk to water in the mixture becomes 8:58 : 5. Find the ratio x:yx : y.

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