Question
150 liters of mixture 'P' (milk + water) contains milk
and water in the ratio of 2:3, respectively. In mixture 'Q' of milk and water, the quantity of milk is 20% more than the quantity of water. 30% and 50% of mixtures 'P' and 'Q', respectively, are mixed to form another mixture 'R', in which the quantity of milk is 10 liters less than the quantity of water. Find the initial quantity of milk and water in mixture 'Q'.Solution
ATQ Ratio of milk and water in mixture 'Q' = 6:5 Let the initial quantity of mixture 'Q' be '110x' liters. In mixture 'R': Quantity of milk = (0.30Ă—150Ă—(2/5))+(0.50Ă—110xĂ—(6/11)) = (18+30x) litres Quantity of water = (0.30Ă—150Ă—(3/5))+(0.50Ă—110xĂ—(5/11)) = (27+25x) litres ATQ; 27 + 25x - (18 + 30x) = 10 Or, 30x - 25x = 27 - 10 - 18 So, 'x' = (1/5) = 0.2 Therefore, initial quantity of mixture 'Q' = '110x' = 110 x 0.2 = 22 liters
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