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Mixtures And Alligations - MCQ 4


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Mixtures And Alligations - MCQ 4 - Question 1

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.

Detailed Solution for Mixtures And Alligations - MCQ 4 - Question 1

Answer – b) 4.4 Explanation : In 1 alloy copper = (1/4)*20 = 5kg and zinc  = (3/4)*20 = 15kg in 2 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)

Mixtures And Alligations - MCQ 4 - Question 2

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.

Detailed Solution for Mixtures And Alligations - MCQ 4 - Question 2

Answer – c) 11:20:44 Explanation : By the rule of allegation, 145                    154
…………165…………….
11                    20
154                  170
………165…………….
5                      11
Final ratio = 11:20:44

Mixtures And Alligations - MCQ 4 - Question 3

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.

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

Answer – c) 1/6 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

Mixtures And Alligations - MCQ 4 - Question 4

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

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

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

Mixtures And Alligations - MCQ 4 - Question 5

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 4 - Question 5

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 4 - Question 6

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.

Detailed Solution for Mixtures And Alligations - MCQ 4 - Question 6

Answer – c) 80% 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%

Mixtures And Alligations - MCQ 4 - Question 7

 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.

Detailed Solution for Mixtures And Alligations - MCQ 4 - Question 7

Answer – c) 47 Explanation : Dry fruit obtained from 150kg of fresh fruit = (25/100)*150 = (80/100)*x.
Solve for x x=47

Mixtures And Alligations - MCQ 4 - Question 8

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.

Detailed Solution for Mixtures And Alligations - MCQ 4 - Question 8

Answer – b) 12.5 Explanation : By using the allegation rule Water: milk = 1:4 = x:50

Mixtures And Alligations - MCQ 4 - Question 9

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 4 - Question 9

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

Mixtures And Alligations - MCQ 4 - Question 10

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 4 - Question 10

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 4 - Question 11

Two varieties of rice costing Rs 25 and Rs 35 respectively are mixed in a certain ration and the resulting mixture is sold at a profit of 20% at Rs 34.8. What is the respective ratio in which they are mixed?

Detailed Solution for Mixtures And Alligations - MCQ 4 - Question 11

C) 3 : 2
Explanation: SP = 34.8, profit = 20%, so CP = (100/120)*34.8 = 29 By method of allegation: 25               35
.        29
6                4
3 : 2

Mixtures And Alligations - MCQ 4 - Question 12

How much quantity of water should be mixed with 10 l of milk costing Rs 50 per litre so that the resultant mixture is to be sold at Rs 44 per kg?

Detailed Solution for Mixtures And Alligations - MCQ 4 - Question 12

D) 1 4/11 litres Explanation: CP of water = Rs 0 By method of allegation: water (x kg)             milk (10 litres) 0                                      50
.                    44
6                                      44
6 : 44
3 : 22
So x/10 = 3/22

Mixtures And Alligations - MCQ 4 - Question 13

In what ratio must the 3 varieties of wheat costing Rs 42, Rs 54 and Rs 65 respectively be mixed so that the resulting mixture is sold for Rs 63.8 at a profit of 10%?

Detailed Solution for Mixtures And Alligations - MCQ 4 - Question 13

E) 7 : 7 : 20
Explanation: SP = 63.8, Profit=10%, so CP = (100/110)*63.8 = 58 Now 58 is greater than 42 and 54 and less than 65 So 42               65
.        58
7                 16
And 54               65
.        58
7                  4
So 1 part of 1st wheat A, 1 part of 2nd wheat B and 2 parts of 3rd wheat C gives A : C = 7 : 16, and B : C = 7 : 4 So A : B : C = 7 : 7 : (16+4) *we have taken 2 parts of C so it is added – when there are 3 varieties to be mixed it is not done like simple calculation of A : C and B : C

Mixtures And Alligations - MCQ 4 - Question 14

A can containing 25 litres of mixture of milk and water has 80% milk in it. How much quantity of the mixture be drawn out and replaced with water such that the new ratio of water to milk becomes 1 : 3?

Detailed Solution for Mixtures And Alligations - MCQ 4 - Question 14

E) 1.5625 litres Explanation: Milk = (80/100)*25 = 20, so water = 5 l So water : milk = 5 : 20 = 1 : 4 Let x litres drawn out So water left = 5 – (1/(1+4))*x = 5 – x/5 Milk left = 20 – (4/(1+4))*x = 20 – 4x/5 Now x litres of water is added too, so water becomes = 5 – x/5 + x = 5 + 4x/5 So [5 + 4x/5] / [20 – 4x/5] = 1/3 75x+12x = 100x-4x 16x = 25 x=25/16 = 1.5625

Mixtures And Alligations - MCQ 4 - Question 15

 A can contains 60 litres of milk. 4 litres of milk is drawn and replaced with water. This procedure is repeated once again. How much quantity of milk is remained in the can?

Detailed Solution for Mixtures And Alligations - MCQ 4 - Question 15

B) 52.26 litres Explanation: Performed 2 times, so Milk left = 60 [1 – 4/60]2

Mixtures And Alligations - MCQ 4 - Question 16

 A variety of wheat costing Rs 8.70 is mixed with another variety in a ratio 2 : 3.If the mixture is sold at Rs 8.10 making a loss of 10%, then what is the cost of 2nd variety of wheat?

Detailed Solution for Mixtures And Alligations - MCQ 4 - Question 16

A) Rs 9.20 Explanation: SP = 8.1, loss = 10%, so CP = (100/90)*8.1 = Rs 9 1st wheat              2nd wheat 8.70                                 x .                   9
2                                    3
So (x – 9)/(9 – 8.70) = 2/3 Solve, x = 9.20

Mixtures And Alligations - MCQ 4 - Question 17

An alloy contains 4 parts bronze and 6 parts copper. How much part of mixture should be drawn out and replaced with bronze so that the ratio of bronze to copper gets reversed in new mixture?

Detailed Solution for Mixtures And Alligations - MCQ 4 - Question 17

B) 1/3
Explanation: Total = 4+ 6 = 10 The old ratio is 4/6 = 2/3, so new ratio of bronze to copper should be 3/2 Let x kg of mixture is drawn out and then x kg of bronze added.
So Bronze is now = 4 – (4/10)*x + x = 4 + (3x/5) Copper is now = 6 – (6/10)*x = 6 – (3x/5) Now [4 + (3x/5)] / [6 – (3x/5)] = 3/2 Solve, x = 10/3 So part of mixture drawn out is (10/3)*10 = 1/3

Mixtures And Alligations - MCQ 4 - Question 18

 Wheat worth Rs 50 per kg and Rs 56 per kg are mixed with a third variety of wheat in the ratio 2 : 2 : 3 respectively. If the mixture obtained is worth Rs 61 per kg. Find the price (per kg) of the third variety of wheat.

Detailed Solution for Mixtures And Alligations - MCQ 4 - Question 18

B) Rs 73 Explanation: Since 1st and 2nd wheat mixed in equal ratio, their average price = (50+56)/2 = Rs 52
Let 3rd variety of wheat be Rs x per kg So they are mixed as : (2+2) : 3 = 4 : 3 So 52                       x .           61
x-61              61-52=9 so x-61/9 = 4/3 solve, x = 73

Mixtures And Alligations - MCQ 4 - Question 19

A mixture of milk and water contains 25% water. 12 litres of this mixture is drawn out and replaced with 5 litres of water. If the new ratio of water to milk becomes 2 : 5, what is the amount of milk originally present in the mixture?

Detailed Solution for Mixtures And Alligations - MCQ 4 - Question 19

E) 84 litres Explanation: Milk : water = 75% : 25% = 3 : 1 Total = 3x+x+12 = 4x+12 So (x+5)/3x = 2/5 Solve, x = 25 So total = 4*25 + 12 = 112 litres So originally milk = 3/(3+1) * 112 = 84

Mixtures And Alligations - MCQ 4 - Question 20

 Mixture A contain water and milk in the ratio 2 : 5 and mixture B contain them in the ratio 3 : 4 respectively. Equal quantities from both the mixture are taken and mixed to form mixture C. What is the ratio of milk to water in mixture C?

Detailed Solution for Mixtures And Alligations - MCQ 4 - Question 20

B) 9 : 5
Explanation: Let x litres taken from both mixtures, Then new ratio of milk to water is [5/(5+2)] * x + [4/(3+4)] * x : [2/(5+2)] * x + [3/(3+4)] * x

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