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    Question

    A mixture (milk + water + honey) contains β€˜12m’

    litres milk, β€˜18n’ litres water and 42 litres more honey than water. If 25% of the mixture was replaced with 6 litres of milk, then the quantity of water in the resultant mixture becomes 10% less than that of milk. Instead, if 25% of the mixture is replaced with 72 litres of honey, then the ratio of the quantity of milk to that of honey will become 1:2. Find the initial quantity of water in the mixture.
    A 105 litres Correct Answer Incorrect Answer
    B 120 litres Correct Answer Incorrect Answer
    C 126 litres Correct Answer Incorrect Answer
    D 125 litres Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    According to the question, If 25% of the mixture was replaced with 6 litres of milk, then the quantity of milk in the resultant mixture = 12m Γ— 0.75 + 6 = (9m + 6) litres. If 25% of the mixture was replaced with 6 litres of milk, then the quantity of water in the resultant mixture = 18n Γ— 0.75 = β€˜13.5n’ litres. ATQ; (9m + 6) Γ— 0.90 = 13.5n Or, 9m + 6 = 13.5n Γ· 0.9 = 15n So, 9m = (15n – 6) – [equation I] If 25% of the mixture was replaced with 72 litres of honey, then the quantity of milk in the resultant mixture = 12m Γ— 0.75 = β€˜9m’ litres. If 25% of the mixture was replaced with 72 litres of honey, then the quantity of honey in the resultant mixture = (18n + 42) Γ— 0.75 + 72 = 13.5n + 31.5 + 72 = (13.5n + 103.5) litres. So, 9m:(13.5n + 103.5) = 1:2 Or, 18m = 13.5n + 103.5 – [equation II] Multiplying equation (I) by β€˜2’, we have: 18m = (30n – 12) So, (30n – 12) = (13.5n + 103.5) [from equation 2] Or, 16.5n = 115.5 So, n = 115.5 Γ· 16.5 = 7 Therefore, the initial quantity of water in the mixture = 18 Γ— 7 = 126 litres.

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