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Mixture and Alligation Test 10
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Mixture and Alligation Test 10
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  • Question 1/20
    1 / -0

    In two alloys copper and zinc are in the ratio of 1:3 and 4:1 respectively. 20 kg of first alloy and 35 kg of second alloy and some quantity of pure zinc is melted together. The final alloy has copper and zinc in the ratio of 5:4. Find the amount of pure zinc melted.

    Solutions

    Explanation :

    In 1st alloy copper = (1/4)*20 = 5kg and zinc  = (3/4)*20 = 15kg

    in 2nd alloy copper = (4/5)*35 = 28kg and zinc = (1/5)*35 = 7kg

    So, 33/(22+x) = 5/4 (X is the amount of pure zinc added)

     

  • Question 2/20
    1 / -0

    In what ratio three kinds of rice costing 1.45rs, 1.54rs and 1.70rs must be mixed so that the mixture can be sold at 1.65rs per kg.

    Solutions

    Explanation :

    By the rule of allegation,

    145                    154

    …………165…………….

    11                    20

    154                  170

    ………165…………….

    5                      11

    Final ratio = 11:20:44

     

  • Question 3/20
    1 / -0

    A container filled with liquid containing 4 parts of water and 6 parts of milk. How much of mixture must be drawn off and filled with water so that the mixture contains half milk and half water.

    Solutions

    Explanation :

    Let water = 40ltr and milk is 60ltr.

    Water = 40 – x*(2/5) + x and milk = 60 – x*(3/5) [x is the amount of mixture taken out] Equate both the equation, we get x = 50/3.

    Now, mixture drawn off = (50/3)/100 =  1/6

     

  • Question 4/20
    1 / -0

    A trader has 1500 kg of wheat. One part of it is sold at 10 percent profit and other part at 18 percent profit. He gains a total of 16 percent on the whole lot. The quantity sold at 10% is-

    Solutions

    Explanation :

    Ratio => 1:3. So quantity sold at 10% = (1/4)*1500 = 375

     

  • Question 5/20
    1 / -0

    Two cans P and Q contains milk and water in the ratio of 3:2 and 7:3 respectively. The ratio in which these two cans be mixed so as to get a new mixture containing milk and water in the ratio 7:4.

    Solutions

    Explanation :

    Milk in 1st can = 3/5 and water = 2/5. Similarly in second can milk = 7/10 and water = 3/10.

    Take the ratio = K:1

    (3k/5 + 7/10)/(2k/5 + 3/10) = 7/4

    Solve for k, we get k = 7/4. So the ratio is 7:4

     

  • Question 6/20
    1 / -0

    A dishonest seller professes to sell his milk at cost price but he mixes water with milk and gains 25 percent, then find the percentage of milk in the mixture.

    Solutions

    Explanation :

    Suppose initially there is 100ltr of milk costing 100 rupees.

    Now he gains 25% means in 100ltr of milk he add 25ltr water, so percentage of milk in the mixture = (100/125)*100 = 80%

     

  • Question 7/20
    1 / -0

    Fresh fruit contains 75 percent water and dry fruit contains 20 percent water. How much dry fruit can be obtained from 150 kg of fresh fruit.

    Solutions

    Explanation :

    Dry fruit obtained from 150kg of fresh fruit = (25/100)*150 = (80/100)*x.

    Solve for x

    x=47

     

  • Question 8/20
    1 / -0

    How much water must be added to 50 litre of milk costing 10 rupees per litre so as to bring the cost of milk to 8 rupees per litre.

    Solutions

    Explanation :

    By using the allegation rule

    Water: milk = 1:4 = x:50

     

  • Question 9/20
    1 / -0

    A trader mixes 6ltr of milk costing 5000 rupees with 7ltr of milk costing 6000 rupees per litre. The trader also mixes some quantity of water to the mixture so as to bring the price to 4800 per litre. How many litres of water is added.

    Solutions

    Explanation :

    (6*5000 + 7*6000)/(13 + w) = 4800 (w is the amount of water added)

     

  • Question 10/20
    1 / -0

    There are three vessels each of 20 litre capacity is filled with the mixture of milk and water. The ratio of milk and water are 2:3, 3:4 and 4:5 respectively. All the vessels are emptied into fourth vessel, then find the ratio of milk and water in the final mixture.

    Solutions

    Explanation :

    Milk = 2/5 + 3/7 + 4/9 and water = 3/5 + 4/7 + 5/9

    so ratio will be 401/544

     

  • Question 11/20
    1 / -0

    A man buys milk at the rate of 5 rupees per litre and mixes it with water. By selling the mixture at Rs 4 a litre he gains 25 percent. How much water did each litre of the mixture contain?

    Solutions

    Explanation :

    By rule of allegation

    Ratio of water: milk = 9:16, so in one litre water will be = 9/25

     

  • Question 12/20
    1 / -0

    A mixture containing milk and water in the ratio 3:2 and another mixture contains them in the ratio 4:5. How many litres of the later must be mixed with 3 litres of the former so that the resulting mixture may contain equal quantities of milk and water?

    Solutions

    Explanation :

    milk = 3*3/5 = 9/5 litre and water = 3*2/5 = 6/5 litre (in first mixture)

    milk = 4k/9 and water = 5k/9 litres in second mixture, so

    9/5 + 4k/9 = 6/5 + 5k/9, we get k = 27/5 litre

     

  • Question 13/20
    1 / -0

    Two vessels contain milk and water in the ratio of 7:3 and 2:3 respectively. Find the ratio in which the contents of both the vessels must be mixed to get a new mixture containing milk and water  in the ratio 3:2.

    Solutions

    Explanation :

    let the ratio be k:1

    then in first mixture, milk = 7k/10 and water = 3k/10

    and in second mixture, milk = 2/5 and water = 3/5

    [7k/10 + 2/5]/[3k/10 3/5] = 3/2

    K = 2, so ratio will be 2:1

     

  • Question 14/20
    1 / -0

    In 80 litre mixture of milk and water, water content is 40 percent. The trader gives 20 litre of the mixture to the customer and adds 20 litres of water to the mixture. What is the final ratio of milk and water in the mixture?

    Solutions

    Explanation :

    milk = 48 and water = 32 litre initially

    then milk = 48 – 20*3/5 = 36 and water = 32 – 20*2/5 + 20 = 44

    so ratio = 9:11

     

  • Question 15/20
    1 / -0

    70 litres of a mixture of milk and water contains 20% water. How much water should be added so that the mixture has 28% water?

    Solutions

    Explanation :

    milk = 56 litre and water = 14 litre. Let x litre of water is added the,

    (14 + x)/(70 + x) = 28/100

     

  • Question 16/20
    1 / -0

    Rice worth Rs. 110 per kg and Rs. 95 per kg are mixed with a third variety in the ratio 1:1:2. If the mixture is worth Rs. 115 per kg, the price of the third variety per kg will be.

    Solutions

    Explanation :

    First two types of rice are mixed in 1:1 so total cost for 2 kg of rice is 205, so average price = 102.5

    So, x – 115 = 12.5, x = 127.5

     

  • Question 17/20
    1 / -0

    A trader has 60 kg of pulses, one part of which is sold at 8% profit and the rest is sold at 14% profit. He gains 12% on whole. What is the quantity sold at 14% profit?

    Solutions

    Explanation :

    So ratio will be 1:2, so quantity sold at 14% profit = 2/3*60 = 40kg

     

  • Question 18/20
    1 / -0

    Two cans of 60 and 80 litres are filled with the mixtures of milk and water. The proportion of milk and water in the cans being 5:7 and 9:7 respectively. If the contents of the two cans are mixed and 30 litres of the water is added to the whole, then find the ratio of milk and water in the final mixture?

    Solutions

    Explanation :

    milk = 60*5/12 = 25 and water = 60*7/12 = 35

    milk = 80*9/16 = 45 and water = 80*7/16 = 35

    milk = 70 and water = 70 + 30 = 100

     

  • Question 19/20
    1 / -0

    There are three vessels each of 20 litre capacity is filled with the mixture of milk and water. The ratio of milk and water are 2:3, 3:4 and 4:5 respectively. All the vessels are emptied into fourth vessel, then find the ratio of milk and water in the final mixture.

    Solutions

    Explanation :

    Milk = 2/5 + 3/7 + 4/9 and water = 3/5 + 4/7 + 5/9

    so ratio will be 401/544

     

  • Question 20/20
    1 / -0

    In two alloys copper and zinc are in the ratio of 1:4 and 3:1 respectively. 20 kg of first alloy and 32 kg of second alloy and some pure zinc are melted together. An alloy is obtained in which the ratio of copper and zinc was 3:5. Find the quantity of zinc melted.

    Solutions

    Explanation :

    Copper = 1/5*20 + 3/4*32 = 28kg

    zinc = 4/5*20 + 1/4*32 = 24kg

    now x kg of zinc is added, so [28/24 + x] = 3/5. X = 68/3 kg

     

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