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- Most Important Multiple Choice Questions
- Online Mixture and Alligation Exercise with Correct Answer Key and Solutions
- Useful for all Competitive Exams
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- Question 1 of 20
1. Question
Gold is 19 times as heavy as water and copper is 9 times heavy. In what ratio must these metals be mixed so that the mixture may be 15 times as heavy as water?
Hint
By the rule of alligation, we have
∴ required ratio
- Question 2 of 20
2. Question
In a mixture of 45 litres, the ratio of milk and water is 3 : 2. How much water must be added to make the ratio 9 : 11?
Hint
Quantity of milk
=
Quantity of water
=
Let x litres of water be added to make the ratio 9 : 11.
∴
⇒ 18 + x = 33
⇒ x =15 litres
- Question 3 of 20
3. Question
In a mixture of 45 litres, the ratio of milk and water is 4 : 1. How much water must be added to make the mixture ratio 3 : 2?
Hint
Quantity of milk
=
= 36 litresQuantity of water
=
= 9 litresLet x litres of water be added to make the ratio 3 : 2
Then,
⇒ 72 = 27 + 3x
⇒ x = 15 litres
- Question 4 of 20
4. Question
A mixture (40 litres) contains tonic and water in the ratio 3 : 1. To make the ratio 7 : 2, how much additional amount of water is required?
Hint
Tonic = 30 litres, Water = 10 litres
Let x litres of water be added, then
⇒ 70 + 7x = 80 + 2x
⇒ 5x = 10
⇒ x = 2 litres.
- Question 5 of 20
5. Question
An alloy contains copper and zinc in the ratio 5 : 3 and another alloy contains copper and tin in the ratio 8 : 5. If equal weights of both the alloys are melted together, then the weight of tin in the resulting alloy per unit will be:
Hint
The first type of alloy does not contain tin. Second type alloy contains tin. Therefore, quantity of tin in 2 units of the resulting alloy = ⁵⁄₁₃
⇒ Quantity of tin in 1 unit of the resulting alloy
=
- Question 6 of 20
6. Question
In three vessels, the ratio of water and milk is 6 : 7, 5 : 9 and 8 : 7, respectively. If the mixtures of the three vessels are mixed together, then what will be the ratio of water and milk?
Hint
Water Milk Total 1st vessel 6 7 13 2nd vessel 5 9 14 3rd vessel 8 7 15 LCM of 13, 14 & 15 = 2730
Increase value of total to 2730 as follows.
1st vessel 1260 1470 2730 2nd vessel 975 1755 2730 3rd vessel 1456 1274 2730 Total 3691 4499 8190 ∴ Required ratio
Alternate method is dividing options by 13, 14 & 15.
- Question 7 of 20
7. Question
A jar of oil was four fifths full. When six bottles of oil were taken out and four bottles of oil were poured into, it was three fourths full. How many bottles of oil were contained by the jar?
Hint
Let the capacity of the jar be of x bottles.
Since 6 bottles were taken out from jar and 4 bottles of oil poured into it
∴ 2 bottles were taken out
Therefore, we have
⇒
⇒
⇒ x = 40
- Question 8 of 20
8. Question
A cane contains a mixture of two liquids A and B in the ratio 7 : 5. When 9 litres of mixture are drawn off and the cane is filled with B, the ratio of A and B becomes 7 : 9. How many litres of liquid A was contained by the cane initially?
Hint
Suppose the cane initially contains 7x and 5x litres of mixtures A and B respectively.
Quantity of A in mixture left
=
Quantity of B in mixture left
=
⇒ 252 x – 189 = 140 x + 147
⇒ 112 x = 336
⇒ x = 3.
So, the cane contained 21 litres of A.
- Question 9 of 20
9. Question
A vessel is fully filled with a special liquid. Four litres of liquid is drawn out of this vessel and is replaced with water. If the ratio of the special liquid to the water becomes 1: 2, then what is the capacity the vessel?
Hint
Let capacity of the vessel be x litres.
Therefore,
∴ x = 6
- Question 10 of 20
10. Question
Two equal glasses filled with mixtures of alcohol and water in the proportions of 2 : 1 and 1 : 1 respectively were emptied into third glass. What is the proportion of alcohol and water in the third glass?
Hint
Alcohol in 1st glass = ⅔;
water in 1st glass = ⅓
Alcohol in 2nd glass = ½ ;
water in 2nd glass = ½
∴ In 3rd glass,
water =
∴ Required ratio
- Question 11 of 20
11. Question
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?
Hint
By alligation rule
∴ The ratio in which the two are to be mixed is
: 
= 3 : 5
- Question 12 of 20
12. Question
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?
Hint
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 13 of 20
13. Question
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?
Hint
Let x gallons of first mixture be mixed with y gallons of second mixture.
Milk Water x gallons (1st) 
y gallons (2nd) 
Third vessel 
Since the third vessel contains half milk and half water,
⇒ 16x + 3y = 2x + 15y
⇒ 16x – 2x = 15y – 3y
Hence
= 14 gallons
- Question 14 of 20
14. Question
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?
Hint
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 15 of 20
15. Question
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.
Hint
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 16 of 20
16. Question
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:
Hint
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 17 of 20
17. Question
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?
Hint
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 18 of 20
18. Question
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?
Hint
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 19 of 20
19. Question
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?
Hint
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 20 of 20
20. Question
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?
Hint
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]