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Mixture and Alligation Test 2
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Mixture and Alligation Test 2
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  • Question 1/10
    1 / -0

    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?

    Solutions

    By alligation rule

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

     : 

    = 3 : 5

  • Question 2/10
    1 / -0

    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?

    Solutions

    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

    ∴ From this equation, we have

    (y = amount of acid initially drawn off)

    ⇒ 

    ⇒ 

    ⇒ 

    ⇒ y = 18 litres

  • Question 3/10
    1 / -0

    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?

    Solutions

    ⇒ 16x + 3y = 2x + 15y

    ⇒ 16x – 2x = 15y – 3y

    Hence 

    = 14 gallons

  • Question 4/10
    1 / -0

    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?

    Solutions

    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

    = 29.16 litres

  • Question 5/10
    1 / -0

    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.

    Solutions

    Ratio of milk in the containers are,

    and the ratio of water in the containers are,

    Ratio of mixture of milk and water in the containers

    =

    = 106 : 230 = 53 : 115

  • Question 6/10
    1 / -0

    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:

    Solutions

    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, 

    ⇒ 

    ⇒ 261 + 2x = 612

    ⇒ 

  • Question 7/10
    1 / -0

    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?

    Solutions

    C.P. of 1 litre of milk

    =

    ∴ Ratio of water and milk

    =

    = 8 : 32 = 1 : 4.

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

    =litres

    = 15 litres.

  • Question 8/10
    1 / -0

    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?

    Solutions

    In mixture,

    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.

  • Question 9/10
    1 / -0

    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?

    Solutions

    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

     =Rs 49

  • Question 10/10
    1 / -0

    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?

    Solutions

    C. P. of mixture

    = 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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