Mixture and Alligation Questions

  1. In a mixture of milk and water of the volume of 80 liter the ratio of milk to water is 3: 2. How much quantity of water will be added to make mixture is equal ?
    16
    15
    12
    18
    20
    Option A
    Quantity of milk in the mixture = 80 * 3/5 = 48
    and water = 80 * 2/5 = 32
    let “x” liter of water to be added,
    48 = 32 + x
    x = 16

     

  2. In what ratio must rice at rs.60 per kg be mixed with rice of rs.74 per kg, so that the mixture must be worth rs.64 per kg ?
    2 : 1
    2 : 5
    4 : 3
    2 : 1
    5 : 2
    Option E
    By using alligetion method,
    60 74
    64
    10 4
    ratio = 5 : 2

     

  3. A vessels contains 80 liters of wine, 20 liters are taken out from vessel is replaced by water and the same process is further replaced two times, then find the quantity of wine left in final solution ?
    12.45 liter
    30.60 liter
    33.75 liter
    40.85 liter
    52.85 liter
    Option C
    Using the formula, wine left over = x ( x – y/x)^n
    = 80 ( 80 – 20/80 )^3
    = 80 ( 3/4)^3 = 80 * 27/64 = 33.75 liter

     

  4. Two alloy A and B are made of copper and zinc in the ratio of 4 : 1 and 4 : 3 respectively. If these two alloys are to be mixed to form a new alloy in which same elements are in the ratio 2 : 1, then what is ratio of alloy A and alloy B in the new alloy ?
    2 : 3
    4 ; 5
    3 : 2
    5 : 7
    3 : 4
    Option D
    By using formula
    4/5 4/7
    2/3
    2/21 2/15
    ratio = 5 : 7

     

  5. In a mixture of wine and water is in the ratio of 5 : 3. If 16 liters of mixtures taken out and replaced with water, so that the ratio of wine and water becomes 3 : 5. Find the initial quantity of wine in the mixture.
    24
    28
    24
    25
    12
    Option D
    Let quantity of wine and water in the mixture is 5x and 3x respectively.
    (5x – 16 * 5/8)/(3x – 16 * 3/8 + 16) = 3/5
    5x – 10/3x – 6 + 16 = 3/5
    5x – 10/3x + 10 = 3/5
    25x – 50 = 9x + 30
    16x = 80
    x = 5
    quantity of wine in the initial mixture = 5 * 5 = 25 liter

     

  6. A vessels contains mixture in which 20% water and rest quantity is milk. If 28 liter of more water is to be added in the vessel , then quantity of water becomes 3/8th of mixture. What is the quantity of milk in the vessel initially ?
    80 liters
    65 liters
    42 liters
    68 liters
    78 liters
    Option A
    Quantity of water = 20%
    quantity of milk = 80%
    ratio = 80 : 20 = 4 : 1
    let quantity of milk and water in the vessel is 4x and x respectively.
    28 liter of water is to be added,
    4x /x + 28 = 5 / 3
    12x = 5x + 140
    7x = 140
    x = 20
    quantity of milk = 4 * 20 = 80 liters

     

  7. Two mixtures A and B in the ratio of juice and water are 3 : 1 and 1 : 2 respectively, mixed in the ratio of 2 : 3. If the juice in final mixture is 48 liter, then find the quantity of water in final mixture ?
    252
    250
    144
    245
    320
    Option A
    By using alligation,
    3/4 1/3
    2/5
    1/15 7/20
    ratio = 4 : 21
    quantity water = 48/4 * 21 = 252 liters

     

  8. A seller mixed sugar cost rs.45 per kg with sugar cost rs. 38 per kg. These mixture he sold at rs.48 per kg so that he can earn 20% profit. Find in what ratio he mixed the two types of sugar ?
    4 : 3
    6 : 7
    2 : 5
    1 : 2
    2 : 3
    Option C
    SP of mixed sugar = 48
    CP of mixed sugar = 48/6 * 5 = 40
    using alligetion method,
    45 38
    40
    2 5
    ratio = 2 : 5

     

  9. A container contains 60 liters of milk 6 liters of milk taken out from this container and replaced by water. This process was replaced further two times. How much amount of milk left in the container ?
    38.28 liters
    43.74 liters
    24.63 liters
    52.68 liters
    42 liters
    Option B
    Using formula,
    x (x – y/x)^n
    = 60 ( 60 – 6/ 60) ^3
    = 60 ( 54/60)^3
    = 60 * 729/1000 = 43.74 liters

     

  10. The ratio of quantity of two varieties of rice of 3 : 2 is mixed. If the of variety of more quantity rice is rs. 15 and the price of the mixture is. rs.16.2 per kg, then find the price of per kg rice which is the less quantity.
    14
    18
    17
    20
    32
    Option B
    Let the price of less quantity rice = x
    = (15 * 3 + x * 2)/ 3 + 2 = 16.2
    45 + 2x = 81
    2x = 81 – 45
    x = 18

     


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