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Mixture and Alligation Exercise 1

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  1. Question 1 of 20
    1. Question

    Gold is 19 times as heavy as water and copper is 9 times heavy. In what ratio must these metals be mixed so that the mixture may be 15 times as heavy as water?

    Hint

    By the rule of alligation, we have

    mixture-and-alligation-q-45447.png

    ∴ required ratio

    mixture-and-alligation-q-45441.png

  2. Question 2 of 20
    2. Question

    In a mixture of 45 litres, the ratio of milk and water is 3 : 2. How much water must be added to make the ratio 9 : 11?

    Hint

    Quantity of milk

    = mixture-and-alligation-q-45483.png

    Quantity of water

    = mixture-and-alligation-q-45477.png

    Let x litres of water be added to make the ratio 9 : 11.

    ∴ mixture-and-alligation-q-45470.png

    ⇒ 18 + x = 33

    ⇒ x =15 litres

  3. Question 3 of 20
    3. Question

    In a mixture of 45 litres, the ratio of milk and water is 4 : 1. How much water must be added to make the mixture ratio 3 : 2?

    Hint

    Quantity of milk

    = mixture-and-alligation-q-45508.png = 36 litres

    Quantity of water

    = mixture-and-alligation-q-45502.png = 9 litres

    Let x litres of water be added to make the ratio 3 : 2

    Then, mixture-and-alligation-q-45496.png

    ⇒ 72 = 27 + 3x

    ⇒ x = 15 litres

  4. Question 4 of 20
    4. Question

    A mixture (40 litres) contains tonic and water in the ratio 3 : 1. To make the ratio 7 : 2, how much additional amount of water is required?

    Hint

    Tonic = 30 litres, Water = 10 litres

    Let x litres of water be added, then

    mixture-and-alligation-q-45521.png

    ⇒ 70 + 7x = 80 + 2x

    ⇒ 5x = 10

    ⇒ x = 2 litres.

  5. Question 5 of 20
    5. Question

    An alloy contains copper and zinc in the ratio 5 : 3 and another alloy contains copper and tin in the ratio 8 : 5. If equal weights of both the alloys are melted together, then the weight of tin in the resulting alloy per unit will be:

    Hint

    The first type of alloy does not contain tin. Second type alloy contains tin. Therefore, quantity of tin in 2 units of the resulting alloy = ⁵⁄₁₃

    ⇒ Quantity of tin in 1 unit of the resulting alloy

    = mixture-and-alligation-q-45567.png

  6. Question 6 of 20
    6. Question

    In three vessels, the ratio of water and milk is 6 : 7, 5 : 9 and 8 : 7, respectively. If the mixtures of the three vessels are mixed together, then what will be the ratio of water and milk?

    Hint
    WaterMilkTotal
    1st vessel6713
    2nd vessel5914
    3rd vessel8715

    LCM of 13, 14 & 15 = 2730

    Increase value of total to 2730 as follows.

    1st vessel126014702730
    2nd vessel97517552730
    3rd vessel145612742730
    Total369144998190

    ∴ Required ratio

    mixture-and-alligation-q-45585.png

    Alternate method is dividing options by 13, 14 & 15.

  7. Question 7 of 20
    7. Question

    A jar of oil was four fifths full. When six bottles of oil were taken out and four bottles of oil were poured into, it was three fourths full. How many bottles of oil were contained by the jar?

    Hint

    Let the capacity of the jar be of x bottles.

    Since 6 bottles were taken out from jar and 4 bottles of oil poured into it

    ∴ 2 bottles were taken out

    Therefore, we have

    ⇒ mixture-and-alligation-q-45737.png

    ⇒ mixture-and-alligation-q-45731.png

    ⇒ x = 40

  8. Question 8 of 20
    8. Question

    A cane contains a mixture of two liquids A and B in the ratio 7 : 5. When 9 litres of mixture are drawn off and the cane is filled with B, the ratio of A and B becomes 7 : 9. How many litres of liquid A was contained by the cane initially?

    Hint

    Suppose the cane initially contains 7x and 5x litres of mixtures A and B respectively.

    Quantity of A in mixture left

    =mixture-and-alligation-q-46045.png

    Quantity of B in mixture left

    =mixture-and-alligation-q-46039.png

    mixture-and-alligation-q-46033.png

    ⇒ 252 x – 189 = 140 x + 147

    ⇒ 112 x = 336

    ⇒ x = 3.

    So, the cane contained 21 litres of A.

  9. Question 9 of 20
    9. Question

    A vessel is fully filled with a special liquid. Four litres of liquid is drawn out of this vessel and is replaced with water. If the ratio of the special liquid to the water becomes 1: 2, then what is the capacity the vessel?

    Hint

    Let capacity of the vessel be x litres.

    Therefore,mixture-and-alligation-q-46008.png

    ∴ x = 6

  10. Question 10 of 20
    10. Question

    Two equal glasses filled with mixtures of alcohol and water in the proportions of 2 : 1 and 1 : 1 respectively were emptied into third glass. What is the proportion of alcohol and water in the third glass?

    Hint

    Alcohol in 1st glass = ⅔;

    water in 1st glass = ⅓

    Alcohol in 2nd glass = ½ ;

    water in 2nd glass = ½

    ∴ In 3rd glass,

    mixture-and-alligation-q-46001.png

    water =mixture-and-alligation-q-45995.png

    ∴ Required ratio

    mixture-and-alligation-q-45988.png

  11. Question 11 of 20
    11. Question

    A mixture of Nitric acid and Sulfuric acid is taken in the ratio of 1 : 2 and another mixture of the same is taken in the ratio 2 : 3. How many parts of the two mixtures must be taken to attain a new mixture consisting of Nitric acid and Sulfuric acid in the ratio of 3 : 5?

    Hint

    By alligation rule

    mixture-and-alligation-q-46107.png

    ∴ The ratio in which the two are to be mixed is

    mixture-and-alligation-q-46101.png : mixture-and-alligation-q-46095.png

    = 3 : 5

  12. Question 12 of 20
    12. Question

    Several litres of acid were drawn off from a 54 litre vessel, full of acid and equal amount of water was added. Again the same volume of the mixture was drawn off and replaced by water. As a result now, the vessel contained 24 litres of pure acid. How much of the acid was drawn off initially?

    Hint

    Let a container contains x units of liquid and y units of liquid is taken out from it. If this operation is repeated n times, then the final quantity of the liquid in the container is

    mixture-and-alligation-q-46089.png.

    ∴ From this equation, we have

    mixture-and-alligation-q-46083.png

    (y = amount of acid initially drawn off)

    ⇒ mixture-and-alligation-q-46076.png

    ⇒ mixture-and-alligation-q-46070.png

    ⇒ mixture-and-alligation-q-46064.png

    ⇒ y = 18 litres

  13. Question 13 of 20
    13. Question

    Two vessels contain mixtures of milk and water in the ratio of 8 : 1 and 1 : 5 respectively. The contents of both of these are mixed in a specific ratio into a third vessel. How much mixture must be drawn from the second vessel to fill the third vessel (capacity 26 gallons) completely in order that the resulting mixture may be half milk and half water?

    Hint

    Let x gallons of first mixture be mixed with y gallons of second mixture.

    MilkWater
    x gallons (1st)mixture-and-alligation-q-46472.pngmixture-and-alligation-q-46466.png
    y gallons (2nd)mixture-and-alligation-q-46460.pngmixture-and-alligation-q-46454.png
    Third vesselmixture-and-alligation-q-46448.pngmixture-and-alligation-q-46442.png

    Since the third vessel contains half milk and half water,

    mixture-and-alligation-q-46436.png

    ⇒ 16x + 3y = 2x + 15y

    ⇒ 16x – 2x = 15y – 3y

    mixture-and-alligation-q-46430.png

    Hence mixture-and-alligation-q-46424.png

    = 14 gallons

  14. Question 14 of 20
    14. Question

    A container contains 40 litres of milk. From this container, 4 litres of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container?

    Hint

    Let a container contains x units of liquid and y units of liquid is taken out from it. If this operation is repeated n times, then the final quantity of the liquid in the container is

    mixture-and-alligation-q-46418.png

    = 29.16 litres

  15. Question 15 of 20
    15. Question

    Three containers A, B and C are having mixtures of milk and water in the ratio 1 : 5, 3 : 5 and 5 : 7, respectively. If the capacities of the containers are in the ratio 5 : 4 : 5, then find the ratio of the milk to the water if the mixtures of all the three containers are mixed together.

    Hint

    Ratio of milk in the containers are,

    mixture-and-alligation-q-46412.png

    and the ratio of water in the containers are,

    mixture-and-alligation-q-46406.png

    Ratio of mixture of milk and water in the containers

    =mixture-and-alligation-q-46399.png

    = 106 : 230 = 53 : 115

  16. Question 16 of 20
    16. Question

    Tea worth Rs 126 per kg and Rs 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs 153 per kg, then the price of the third variety per kg is:

    Hint

    Let the third type of tea is priced at Rs x per kg. Also suppose that the three types of tea mixed together are ℓ, ℓ and 2 kg,respectively.

    Now, mixture-and-alligation-q-46711.png

    ⇒ mixture-and-alligation-q-46705.png

    ⇒ 261 + 2x = 612

    ⇒ mixture-and-alligation-q-46699.png

  17. Question 17 of 20
    17. Question

    How much water must be added to 60 litres of milk at 1½ litres for Rs 20 so as to have a mixture worth Rs 10⅔ a litre?

    Hint

    C.P. of 1 litre of milk

    =mixture-and-alligation-q-47106.png

    mixture-and-alligation-q-47100.png

    ∴ Ratio of water and milk

    =mixture-and-alligation-q-47093.png

    = 8 : 32 = 1 : 4.

    ∴ Quantity of water to be added to 60 litres of milk

    =mixture-and-alligation-q-47087.pnglitres

    = 15 litres.

  18. Question 18 of 20
    18. Question

    Pure milk costs Rs 3.60 per litre. A milkman adds water to 25 litres of pure milk and sells the mixture at Rs 3 per litre. How many litres of water does he add?

    Hint

    In mixture,

    mixture-and-alligation-q-47069.png

    Since in every 5 litres of milk, he adds 1 litre of water.

    ∴ In every 25 litres of milk, he adds 5 litres of water.

  19. Question 19 of 20
    19. Question

    Sameer bought 10 kg of tea at Rs 45 per kg and 8 kg at Rs 50 per kg. He mixed both the brands and sold it at a total profit of Rs 32. What was the selling price per kg of the mixture?

    Hint

    C. P. of mixture of 18 kg

    = 10 × 45 + 8 × 50 = Rs 850

    ∴ S. P. = C. P. + profit

    = 850 + 32 = Rs 882

    ∴ S. P. = Rs 882 for 18 kg

    ∴ S. P. for 1 kg

    mixture-and-alligation-q-47063.png =Rs 49

  20. Question 20 of 20
    20. Question

    A mixture consists of 15 parts of coffee, purchased at Rs 2.10 per kg and 1 part of chicory, purchased at 98 paise per kg. If it is sold at Rs 2.25 per kg, what profit would be made on the sale of 5 quintals?

    Hint

    C. P. of mixture

    mixture-and-alligation-q-47443.png

    = Rs 2.03 per kg

    Profit on 1 kg of mixture

    = Rs (2.25 – 2.03) = Rs 0.22

    ∴ profit on 5 quintals mixture

    = 0.22 × 500 = Rs 110

    [since 1 quintal = 100 kg]

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