8 Mixtures & Solutions
Step 4: Since the alcohol solution is replaced, we need to subtract and add
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Original – removed + added = result 0.15 × 10 – 0.15 × x + 0.8 × x = 0.7 × 10 1.5 – 0.15x + 0.8x = 7
Isolate variable x 0.8x – 0.15x = 7 – 1.5 0.65x = 5.5
Hence 8.46 gallons of alcohol solution needs to be replaced.
Some Important Results:
When two or more ingredients (I1, I2, I3…..In)
are mixed such that the
mixture contains x1 quantity of ingredient I1 of unit cost C1, x2 quantity of ingredient I2 of unit cost C2 and so on then the average Mean Cost Cm is defined as
Cm =
When two mixtures M1 and M2, each containing ingredients A and B in the ratio a:b and x:y respectively, are mixed, the proportion of the ingredients A and B i.e., Qa : Qb, in the compound mixture is given by:
And, the quantity in which M1 and M2 is to be mixed when the quantity of A and B i.e. Qa and Qb in the compound mixture is known is given by:
If a vessel contains 'x' litres of liquid A, and 'y' liters be withdrawn and replaced by liquid B, then if 'b' litres of mixture be withdrawn and replaced by liquid B, and the operation is repeated 'n' times in all, then:
Example:
From a vessel containing 64 litres of milk, 8 litres are drawn out and the vessel is filled up with water.
If the same operation is repeated a second time then a third time, how many liters of milk will be left in the cask? What will be the proportion of milk to water in the resulting mixture?
Solution:
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1. From 100 litres of milk water solution, we remove 10 litres of the solution and then we add 10 liters of water. Final milk water ratio comes out to be 3:7. Find the initial milk water ratio?
a. 1:2 b. 11:23 c. 22:45 d. 33:67
2. From 100 liters of milk water ratio, we add 10 liters of water and then we remove 10 liters of solution and final milk water ratio comes out to be 3:7. What was the initial milk water ratio?
a. 1:2 b. 11:23 c. 22:45 d. 33:67
3. We have two beakers of equal capacity. First beaker contains pure milk and second beaker contains pure water. We transfer half the content of the first beaker into second beaker followed by transferring the same quantity from the second beaker to the first beaker. And then the same process was repeated. What will be final ratio of milk and water in the second beaker?
a. 4:5 b. 5:4 and simultaneously an equal amount of water was transferred to first beaker from second beaker. Finally it was realized that now both the beakers contain same ratio of milk and water. What was the quantity transferred?
a. 1 litres b. 2 litres
c. 3 litres d. None of the above 5. We have 100 litres of pure milk solution. 10
litres of the solution replaced by water thrice.
What is the final concentration of milk in the solution?
a. 70 % b. 72.9 %
c. 81 % d. 67 %
6. There are two beakers with 100 ml of milk in first beaker and 100 ml of water in the second beaker. Now 10 ml is transferred from first beaker to second beaker followed by transferring of 10 ml from second beaker to the first beaker.
This is followed by transferring 20 ml from first beaker to second beaker followed by transferring 20 ml form second beaker to the first beaker.
Then which of the following statements is true?
a. Milk to water ratio in first beaker will be more than water to milk ratio in the second beaker
b. Milk to water ratio in first beaker will be less than water to milk ratio in the second beaker
c. Milk to water ratio in first beaker will be equal to water to milk ratio in the second beaker
d. None of the above
7. A substance is 99% water. Some water evaporates, leaving a substance that is 98%
water. How much of the water evaporated?
a. 1 % b. 10 %
c. 5 % d. 50 %
8. There is 100 litres of 50 % milk solution. Half of the solution is removed and replaced with milk. Then one third of the solution is removed and replaced with milk. Finally one fourth of the solution was removed and replaced with milk. Now, what is the concentration of milk in the final solution?
a. 25 % b. 75 % c. 87.5 % d. 12.5 %
9. We have a 100 litres solution of 50 % milk solution. How many times 10 litres of this
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solution can be replaced with water to ensure at least 30% milk solution?
a. 3 b. 4
c. 5 d. 6
10. We had a 750 ml pure alcohol solution, X ml of this solution was replaced with water twice and finally this solution had only 607.5 ml of alcohol. What is the value of x?
a. 25 ml b. 50 ml c. 71.25 ml d. 75 ml
11. In a sodium water solution, there was 20 % sodium and 80 % water. If 2 KG of water has evaporated with time and 2 KG of sodium is added to the solution, concentration of sodium has increased to 40%. Initially, what was the total weight of the solution?
a. 8 KG b. 10 KG
c. 12 KG d. 15 KG
12. 10 ml of a pure whiskey solution was replaced by water and then this process was repeated.
Finally water to whiskey ratio in the peg was 9:16. What was the amount of complete peg?
a. 50 ml b. 100 ml c. 150 ml d. 200 ml
13. A milk man mixes 10 litres of water in 90 litres of milk. If he sells one third of these solutions and replenishes it with water then what part of the complete solution is milk now?
a. 30 % b. 50 %
c. 60 % d. 80 %
14. From a container of 800 litres containing pure milk, 80 litres of milk is replaced with water and this process is repeated twice. What will be the final concentration of milk in the solution?
a. 81% b. 72.9%
c. 64.8% d. 58.32%
15. Two mixtures of milk and water in the ratio 1:2 and 1:3 are mixed in equal quantity. What will be milk water ratio in this final mixture?
a. 2:5 b. 5:14
c. 7:17 d. 9:23
16. How much water should be added to 1 litre of 2% acid concentration to decrease the acid concentration to 1%?
a. 0.1 litre b. 0.5 litre c. 0.9 litre d. 1 litre
17. What percentage of a milk solution was water if a milk man makes 10 % profit by selling milk at his cost price?
a. 10 % b. 9.09 %
c. 11.11% d. None of the above 18. What part of a 3:2 milk water solution should
be replaced with water in order to reverse the ratio of milk and water?
a. Half b. One third c. One fourth d. One fifth
19. Chaman purchased two types of apples: first at Rs 40 per Kg and second at Rs 60 per Kg.
He mixed both the apples and sold all of them at Rs 50 per Kg. What will be his net profit or loss if he spends equal amount of money on both of them?
He mixed both the apples and sold all of them at Rs 50 per Kg. What will be his net profit or loss if he purchased equal quantity of both types of apples? ratio should the contents of these two vessels be mixed such that the resultant mixture has whisky and soda in the ratio of 2 : 5?
a. 31 : 25 b. 9 : 26
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c. 26 : 63 d. 26 : 9
22. A vessel is completely filled with beer. 10 litres are drawn from the vessel and replaced with water. 10 litres of this mixture is then drawn and replaced with water. Find the capacity of the vessel if the ratio of beer to water is 16:9 at the end.
a. 60 ltrs. b. 36 ltrs.
c. 50 ltrs. d. 46 ltrs.
23. Sixty litres of wine is drawn from 600 litres of wine and replaced by water. 60 ltrs of mixture is again drawn and replaced with water and this process is repeated once more. Find the present quantity of wine in the mixture.
a. 420 ltrs. b. 393.66 ltrs.
c. 486 ltrs. d. 437.4 ltrs.
24. A vessel has 90 litres of a mixture of milk and water containing 10% water. If x litres of water is added to the vessel, the ratio of milk and water would be reversed. Instead, if y litres of milk is removed from the vessel(assume that it is possible to separate milk and water in a solution), the ratio of milk and water would be reversed. Find (x–y). Rs. 10 more than variety B, what is the cost of variety B per kg?
a. Rs. 34 b. Rs. 54 c. Rs. 44 d. Rs. 64
26. The price per kg of mangoes has trebled. If Dheeraj wants to keep his expenditure same, by what percentage should his consumption decrease.
a. 100% b. 66.67%
c. 33.33% d. 200%
27. 750 candidates appeared in an examination. 70%
of the girls and 65% of the boys passed the
examination. If the total pass percentage was 67%, find the number of boys that appeared in the examination.
a. 350 b. 420
c. 300 d. 450
28. A 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2. 10 litres of the mixture is removed and replaced with pure milk and the operation is repeated once more. At the end of the two replacements, what is the ratio of milk and water in the resultant mixture?
a. 17 : 3 b. 9 : 1 c. 3 : 17 d. 5 : 3
29. In which of the following ratios must a person mix three kinds of tea costing Rs. 60/kg, Rs. 75/
kg and Rs. 100/kg so that the resultant mixture when sold at Rs. 96/kg yields a profit of 20%?
a. 1 : 2 : 4 b. 3 : 7 : 6 c. 1 : 4 : 2 d. None of these
30. A merchant mixes three varieties of rice costing Rs.20/kg, Rs.24/kg and Rs.30/kg and sells the mixture at a profit of 20% at Rs.30/kg. How many kgs of the second variety will be in the mixture if 2 kgs of the third variety is there in the mixture?
a. 1 kg b. 5 kgs
c. 3 kgs d. Cannot be determined 31. How many litres of water should be added to
a 30 litre mixture of milk and water containing milk and water in the ratio of 7 : 3 such that the resultant mixture has 40% water in it?
a. 7 litres b. 10 litres c. 5 litres d. None of these
32. How many kgs of Basmati rice costing Rs.42/
kg should a shopkeeper mix with 25 kgs of ordinary rice costing Rs.24 per kg so that he makes a profit of 25% on selling the mixture at Rs.40/kg?
a. 20 kgs b. 12.5 kgs
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c. 16 kgs d. 200 kgs
33. How many litres of a 12 litre mixture containing milk and water in the ratio of 2: 3 be replaced with pure milk so that the resultant mixture contains milk and water in equal proportion?
a. 4 litres b. 2 litres c. 2.5 litres d. 3 litres
34. A sample of x litres from a container having a 60 litre mixture of milk and water containing milk and water in the ratio of 2 : 3 is replaced with pure milk so that the container will have milk and water in equal proportions. What is the value of x?
a. 6 litres b. 10 litres c. 30 litres d. None of these
35. A zookeeper counted the heads of the animals in a zoo and found them to be 80. When he counted the legs of the animals he found them to be 260. If the zoo had either pigeons or horses, how many horses were there in the zoo?
a. 60 b. 20
c. 50 d. 70
36. From a cask of milk containing 30 litres, 6 litres are drawn out and the cask is filled up with water. If the same process is repeated a second, then a third time, what will be the number of litres of milk left in the cask?
a. 0.512 litres b. 13 litres c. 15 litres d. 15.36 litres
37. A bucket having a capacity of 100 litres is full of milk. 10 litres of milk is removed and replaced with water. This process is repeated 2 more times. Find the final quantity of milk removed from the bucket?
a. 27.1 lts. b. 32 lts.
c. 25 lts. d. 72.9 lts.
38. A flask is full of milk. 10 litres of milk is removed from the flask and replaced with water.
This is done one more time. The proportion of milk in the bucket becomes . Find the capacity of bucket?
a. 25 b. 45
c. 20 d. 24
39. One alloy of brass is composed of tin, copper and zinc in the ratio of 2:15: 5. Another alloy of brass contains these metals in the ratio of 7 : 23 : 3. Equal weights of these alloys are taken and fused together. What is the ratio of these ingredients in the resulting alloy?
a. 20:91:21 b. 19:20:12 c. 91:20:21 d. 10:20:31
40. Three containers A, B and C are having mixtures of milk and water in the ratio of 1 : 5, 3 : 5 and 5 : 7 respectively. If the capacities of the containers are in the ratio 5: 4: 5, find the ratio of milk to water, if the mixtures of all the three containers are mixed together. taken from each to form a mixture which shall contain 6 kg of coffee and 3 kg of chicory (in kg respectively)?
a. 4, 6 b. 5, 6 c. 4, 5 d. 6, 7
42. A mixture contains milk & water in the ratio 5:1 on adding 5 litres of water, the ratio of milk and water becomes 5 : 2. Find the quantity of milk in the original mixture.
a. 20 lt b. 25 lt c. 30 lt d. 28 lt
43. A 50 ml after–shave lotion containing 30%
alcohol is mixed with 30 ml of pure water.
What is the percentage of alcohol in the new solution?
a. 20% b. 22%
c. 15% d. 18.75%
44. You add x ml of a 25% alcohol solution to a 200 ml of a 10% alcohol solution to obtain another solution. Find x so that the final solution has a alcohol percentage of 15%.
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a. 100 b. 150
c. 300 d. 200
45. In what ratio must milk be added with water so as to gain 20% by selling the mixture at cost price of pure milk?
a. 1 : 4 b. 1 : 3 c. 1 : 5 d. 1 : 6
46. There is a milk water solution with milk water ratio as 1:4. What is the minimum number of times, that 10 % of the solution should be removed and replaced with water in order to reduce the milk water ratio to less than 1:8?
a. 5 b. 6
c. 7 d. 8
47. A beaker contains milk and water in the ratio 4:1. 10 litres of this solution is replaced with water and the milk water ratio becomes 3:2. What will be the final volume of the beaker?
a. 40 litres b. 50 litres c. 75 litres d. 100 litres
48. There is a beaker with 80 liters of 20%
milk solution. How much pure milk should be added to the solution to make it 25% milk solution?
a. 4 ltr. b. 5 ltr.
c. 5.33 ltr. d. 5.66 ltr.
49. There is a holy beaker of spirit which contains 100 ltr. of 50% spirit solution. Every week 10%
of the spirit in the solution is evaporated and this need to be made up by adding 5 liters of pure spirit to the solution every Sunday. On particular Sunday, pure spirit was not added to the solution then how much spirit should be added next week to make up for the evaporated spirit during the course of two weeks?
a. 8 ltr. b. 9.5 ltr.
c. 10 ltr. d. 10.5 ltr.
50. 5 litres of a pure water solution is replaced with pure milk twice and finally water milk ratio becomes 49:576. Find the total quantity of the solution.
a. 250 ltr. b. 100 ltr.
c. 125 ltr. d. None of the above