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Quiz: Mixture & Alligation

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Number of Questions: 50

Question: 1 -

A mixture of 150 liters of wine and water contains 20% water. How much more water should be added so that water becomes 25% of the new mixture?

Options:

  1. 7 liters

  2. 9 liters

  3. 10 liters

  4. 15 liters

    5. Answer:

    10 liters
    Solution:

    Number of liters of water in150 liters of the mixture = 20% of 150 = 20/100 * 150 = 30 liters.
    P liters of water added to the mixture to make water 25% of the new mixture.
    Total amount of water becomes (30 + P) and total volume of mixture is (150 + P).
    (30 + P) = 25/100 * (150 + P)
    120 + 4P = 150 + P => P = 10 liters.

Question: 2 -

In a can, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 6 : 5. Find the capacity of the can?

Options:

  1. 48

  2. 52

  3. 44

  4. 40

    5. Answer:

    44
    Solution:

    Let the capacity of the can be T litres.

    Quantity of milk in the mixture before adding milk = 4/9 (T - 8)
    After adding milk, quantity of milk in the mixture = 6/11 T.
    6T/11 - 8 = 4/9(T - 8)
    10T = 792 - 352 => T = 44.

Question: 3 -

 In a mixture of milk and water, the proportion of milk by weight was 80%. If, in a 180 gm mixture, 36 gms of pure milk is added, what would be the percentage of milk in the mixture formed?

Options:

  1. 87.5%

  2. 100%

  3. 80%

  4. None of these

    5. Answer:

    None of these
    Solution:

    Percentage of milk in the mixture formed = [80/100 (180) + 36] / (180 + 36) * 100% = (144 + 36)/216 * 100% = 5/6 * 100% = 83.33%.

Question: 4 -

A vessel contains 20 liters of a mixture of milk and water in the ratio 3:2. 10 liters of the mixture are removed and replaced with an equal quantity of pure milk. If the process is repeated once more, find the ratio of milk and water in the final mixture obtained?

Options:

  1. 3:5

  2. 7:8

  3. 9:1

  4. 1:2

    5. Answer:

    9:1
    Solution:

    Milk = 3/5 * 20 = 12 liters, water = 8 liters
    If 10 liters of mixture are removed, amount of milk removed = 6 liters and amount of water removed = 4 liters.
    Remaining milk = 12 - 6 = 6 liters
    Remaining water = 8 - 4 = 4 liters
    10 liters of pure milk are added, therefore total milk = (6 + 10) = 16 liters.
    The ratio of milk and water in the new mixture = 16:4 = 4:1
    If the process is repeated one more time and 10 liters of the mixture are removed, then amount of milk removed = 4/5 * 10 = 8 liters.
    Amount of water removed = 2 liters.
    Remaining milk = (16 - 8) = 8 liters.
    Remaining water = (4 -2) = 2 liters.
    The required ratio of milk and water in the final mixture obtained = (8 + 10):2 = 18:2 = 9:1.

Question: 5 -

 Two varieties of wheat - A and B costing Rs. 9 per kg and Rs. 15 per kg were mixed in the ratio 3 : 7. If 5 kg of the mixture is sold at 25% profit, find the profit made?

Options:

  1. Rs. 14.50

  2. Rs. 13.50

  3.  Rs. 16.50

  4. Rs. 15.50

    5. Answer:

     Rs. 16.50
    Solution:

    Let the quantities of A and B mixed be 3x kg and 7x kg.

    Cost of 3x kg of A = 9(3x) = Rs. 27x
    Cost of 7x kg of B = 15(7x) = Rs. 105x
    Cost of 10x kg of the mixture = 27x + 105x = Rs. 132x
    Cost of 5 kg of the mixture = 132x/10x (5) = Rs. 66
    Profit made in selling 5 kg of the mixture = 25/100 (cost of 5 kg of the mixture) = 25/100 * 66 = Rs. 16.50