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Mixtures And Alligations - MCQ 3


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Mixtures And Alligations - MCQ 3 - Question 1

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?

Detailed Solution for Mixtures And Alligations - MCQ 3 - Question 1

Answer –a) 9/25 Explanation : By rule of allegation Ratio of water: milk = 9:16, so in one litre water will be = 9/25

Mixtures And Alligations - MCQ 3 - Question 2

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?

Detailed Solution for Mixtures And Alligations - MCQ 3 - Question 2

Answer – d) 5.2/5 litre 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

Mixtures And Alligations - MCQ 3 - Question 3

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.

Detailed Solution for Mixtures And Alligations - MCQ 3 - Question 3

Answer – a) 2:1 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

Mixtures And Alligations - MCQ 3 - Question 4

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?

Detailed Solution for Mixtures And Alligations - MCQ 3 - Question 4

Answer – b) 9:11 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

Mixtures And Alligations - MCQ 3 - Question 5

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?

Detailed Solution for Mixtures And Alligations - MCQ 3 - Question 5

Answer –c) 70/9 litre Explanation : milk = 56 litre and water = 14 litre. Let x litre of water is added the, (14 + x)/(70 + x) = 28/100

Mixtures And Alligations - MCQ 3 - Question 6

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

Detailed Solution for Mixtures And Alligations - MCQ 3 - Question 6

Answer –b) 127.5 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

Mixtures And Alligations - MCQ 3 - Question 7

 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?

Detailed Solution for Mixtures And Alligations - MCQ 3 - Question 7

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

Mixtures And Alligations - MCQ 3 - Question 8

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?

Detailed Solution for Mixtures And Alligations - MCQ 3 - Question 8

Answer – b) 7:10 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

Mixtures And Alligations - MCQ 3 - Question 9

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.

Detailed Solution for Mixtures And Alligations - MCQ 3 - Question 9

Answer – b) 401/544 Explanation : Milk = 2/5 + 3/7 + 4/9 and water = 3/5 + 4/7 + 5/9 so ratio will be 401/544

Mixtures And Alligations - MCQ 3 - Question 10

 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.

Detailed Solution for Mixtures And Alligations - MCQ 3 - Question 10

Answer – c) 68/3 kg 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

Mixtures And Alligations - MCQ 3 - Question 11

An alloy contains iron, copper and zinc in the ratio of 3:4:2. Another alloy contains copper, zinc and tin in the ratio of 10:5:3. If equal quantities of both alloys are melted, then weight of tin per kg in the new alloy

Detailed Solution for Mixtures And Alligations - MCQ 3 - Question 11

Answer – c) 1/12 kg Explanation : I:C:Z = 3:4:2 (in first alloy) and C:Z:T = 10:5:3 Equal quantities is taken. So, I:C:Z = 6:8:4 in first alloy and C:Z:T = 10:5:3 I = 6
C = 8 + 10 = 18
Z = 4+5 = 9
T = 3
So weight of tin = 3/36 = 1/12

Mixtures And Alligations - MCQ 3 - Question 12

8 litres are drawn from a flask containing milk and then filled with water. The operation is performed 3 more times. The ratio of the quantity of milk left and total solution is 81/625. How much milk the flask initially holds?

Detailed Solution for Mixtures And Alligations - MCQ 3 - Question 12

Answer – b) 20ltr Explanation : let initial quantity be Q, and final quantity be F F = Q*(1 – 8/Q)^4
81/625 = (1-8/Q)^4
3/5 = 1 – 8/Q
Q = 20

Mixtures And Alligations - MCQ 3 - Question 13

A 40 litre mixture contains milk and water in the ratio of 3:2. 20 litres of the mixture is drawn of and filled with pure milk. This operation is repeated one more time. At the end what is the ratio of milk and water in the resulting mixture?

Detailed Solution for Mixtures And Alligations - MCQ 3 - Question 13

Answer – d) 9:1 Explanation : milk = 40*3/5 = 24 and water  = 16 litres initially milk = 24 – 20*3/5 + 20 = 32 – 20*4/5 + 20 = 36 water = 16 – 20*2/5 = 8 – 20*1/5 = 4

Mixtures And Alligations - MCQ 3 - Question 14

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.

Detailed Solution for Mixtures And Alligations - MCQ 3 - Question 14

Answer – a) 2:1 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

Mixtures And Alligations - MCQ 3 - Question 15

How many Kgs of rice A costing rupees 20 per kg must be mixed with 20 kg of rice B costing rupees 32 per kg, so that after selling them at 35 rupees per kg, he gets a profit of 25%.

Detailed Solution for Mixtures And Alligations - MCQ 3 - Question 15

Answer – a) 10 kg Explanation : by rule of alligation, 20           32
…….28………..
4            8
So, x = 10

Mixtures And Alligations - MCQ 3 - Question 16

How many litres of water must be added to 60 litre mixture that contains milk and water in the 7:3 such that the resulting mixture has 50% water in it?

Detailed Solution for Mixtures And Alligations - MCQ 3 - Question 16

Answer – c) 24 Explanation : milk = (7/10)*60 = 42 and water = 18 so water must be added = 42 – 18 = 24

Mixtures And Alligations - MCQ 3 - Question 17

 A sample of x litre is replaced from a container containing milk and water in the ratio 2:3 by pure milk. If the container hold 30 litres of the mixture, and after the operation proportion of milk and water is same. Find the value of X?

Detailed Solution for Mixtures And Alligations - MCQ 3 - Question 17

Answer – b) 5 Explanation : milk = 30*2/5 = 12 and water = 30*3/5 = 18 milk = 12 – x*2/5 + x and water = 18 – x*3/5 equate both equation and we get x = 5

Mixtures And Alligations - MCQ 3 - Question 18

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.

Detailed Solution for Mixtures And Alligations - MCQ 3 - Question 18

Answer – c) 7:4 Explanation : Milk in 1 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

Mixtures And Alligations - MCQ 3 - Question 19

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

Detailed Solution for Mixtures And Alligations - MCQ 3 - Question 19

Answer – b) 2ltr Explanation : (6*5000 + 7*6000)/(13 + w) = 4800 (w is the amount of water added)

Mixtures And Alligations - MCQ 3 - Question 20

How many kilograms of rice costing Rs. 9 per kg must be mixed with 27kg of rice costing Rs.7 per kg so that there may be gain of 10% by selling the mixture at Rs.9.24 per kg?

Detailed Solution for Mixtures And Alligations - MCQ 3 - Question 20

Answer – a) 63 Explanation : By rule of allegation: – 9        7
….8.4…..
1.4     0.6
So, x/27 = 1.4/0.6, we get x = 63 kg

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