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Quiz: Mixture & Alligation

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Number of Questions: 50

Question: 6 -

A vessel of capacity 90 litres is fully filled with pure milk. Nine litres of milk is removed from the vessel and replaced with water. Nine litres of the solution thus formed is removed and replaced with water. Find the quantity of pure milk in the final milk solution?

Options:

  1. 74.7

  2. 73.8

  3. 72.9

  4. 72

    5. Answer:

    72.9
    Solution:

    Let the initial quantity of milk in vessel be T litres.

    Let us say y litres of the mixture is taken out and replaced by water for n times, alternatively.
    Quantity of milk finally in the vessel is then given by [(T - y)/T]n * T 
    For the given problem, T = 90, y = 9 and n = 2.
    Hence, quantity of  milk finally in the vessel 
    = [(90 - 9)/90]2 (90) =  72.9 litres.

Question: 7 -

In what ratio should a variety of rice costing Rs. 6 per kg be mixed with another variety of rice costing Rs. 8.75 per kg to obtain a mixture costing Rs. 7.50 per kg?

Options:

  1. 7:8

  2. 4:5

  3.  8:9

  4. 5:6

    5. Answer:

    5:6
    Solution:

    Let us say the ratio of the quantities of cheaper and dearer varieties = x : y

    By the rule of allegation, x/y = (87.5 - 7.50) / (7.50 - 6) = 5/6

Question: 8 -

Two vessels P and Q contain 62.5% and 87.5% of alcohol respectively. If 2 litres from vessel P is mixed with 4 litres from vessel Q, the ratio of alcohol and water in the resulting mixture is?

Options:

  1. 16:7

  2.  16 : 5

  3. 19:5

  4. 14:5

    5. Answer:

    19:5
    Solution:

    Quantity of alcohol in vessel P = 62.5/100 * 2 = 5/4 litres

    Quantity of alcohol in vessel Q = 87.5/100 * 4 = 7/2 litres
    Quantity of alcohol in the mixture formed = 5/4 + 7/2 = 19/4 = 4.75 litres
    As 6 litres of mixture is formed, ratio of alcohol and water in the mixture formed = 4.75 : 1.25 = 19 : 5.

Question: 9 -

A mixture of 70 litres of milk and water contains 10% water. How many litres of water should be added to the mixture so that the mixture contains 12 1/2% water?

Options:

  1. 8

  2. 6

  3. 2

  4. 4

    5. Answer:

    2
    Solution:

    Quantity of milk in the mixture = 90/100 (70) = 63 litres.

    After adding water, milk would form 87 1/2% of the mixture.
    Hence, if quantity of mixture after adding x liters of water, (87 1/2) / 100 x = 63 => x = 72
    Hence 72 - 70 = 2 litres of water must be added.

Question: 10 -

 All the water in container A which was filled to its brim was poured into two containers B and C. The quantity of water in container B was 62.5% less than the capacity of container A. If 148 liters was now transferred from C to B, then both the containers would have equal quantities of water. What was the initial quantity of water in container A?

Options:

  1. 888

  2. 1184

  3. 648

  4. 928

    5. Answer:

    1184
    Solution:

    B has 62.5% or (5/8) of the water in A. Therefore, let the quantity of water in container A(initially) be 8k.

    Quantity of water in B = 8k - 5k = 3k.
    Quantity of water in container C = 8k - 3k = 5k
    Container:               A   B    C
    Quantity of water: 8k  3k   5k
    It is given that if 148 liters was transferred from container C to container B, then both the containers would have equal quantities of water.
    5k - 148 = 3k + 148 => 2k = 296 => k = 148
    The initial quantity of water in A = 8k = 8 * 148 = 1184 liters.