Alligation Method: It refers to a rule that helps to find ratio in which two or three ingredients at a given price are mixed to produce a mixture of specified price.
1. Equal quantities of two milk and water solutions which contains milk and water in ratio, 1 : 5 and 3 : 5 are mixed together. What will be the ratio of water to milk in the resultant solution?
a) 13 : 35 b) 4 : 10 c) 5 : 8 d) 35 : 13
Ans: d
2. The respective ratio of milk and water in 66 litres of adulterated milk is 5 : 1. Water is added into it to make the respective ratio 5 : 3. What is the quantity of water added?
a) 11 litres b) 22 litres c) 33 litres d) 44 litres
Ans: b
3. A 200 litres solution of alcohol and water contains 1/4 th part alcohol. Find the new percentage of alcohol, if 50 litres of the original solution is replaced by 50 litres of alcohol.
a) 43.75% b) 50% c) 66.66% d) 80%
Ans: a
4. A container has 80 litres of milk. From this container 8 litres of milk was taken out and replaced with water. The process was further repeated twice. How much milk is there in the container finally? (in liters)
a) 58.32 b) 60.32 c) 62 d) 64.7
Ans: a
5. 100 litres of a mixture contains 10% water and the rest milk. The amount of water that must be added so that the resulting mixture contains only 50% milk is......
a) 70 litres b) 72 litres c) 78 litres d) 80 litres
Ans: d
6. In a particular type of fertilizer, the ratio of two chemicals A and B is 2 : 5. In 21 kg of this fertilizer, if 3 kg of type - A is added, the ratio of chemical A to B in the new fertilizer will be
a) 1 : 1 b) 2 : 3 c) 3 : 5 d) 4 : 5
Ans: c
7. Rice worth Rs.120 per kg and Rs.132 per kg are mixed with a third variety in the ratio 2 : 1 : 3. If the mixture is worth Rs.135 per kg, the price of the third variety per kg will be....
a) Rs.140 b) Rs.146 c) Rs.150 d) Rs.148
Ans: b
8. A jar full of wine contains 50% alcohol. A part of wine is replaced by another containing 20% alcohol and now percentage of alcohol was found to be 30%. The part of wine replaced is?
a) 1/2 b) 1/3 c) 2/5 d) 2/3
Ans: d
9. A shopkeeper has 50 kg rice, a part of which he sells at 10% profit and rest at 25% profit. He gains 16% on the whole. The quantity sold at 10% profit is?
a) 30 kg b) 20 kg c) 45 kg d) 27 kg
Ans: a
10. An alloy contains tin, copper and zinc in ratio 2 : 3 : 1, and another alloy contain copper, aluminium and tin in ratio 3 : 2 : 7. If both alloys are mixed in equal quantities, then what will be the ratio of tin and aluminium in final alloy?
a) 2 : 11 b) 11 : 9 c) 9 : 2 d) 11 : 2
Ans: d
Model Questions
1. A container contains 60 litres of milk. From this container 6 litres of milk was taken out and replaced by water. This process was repeated further two times. How much milk (in litres) is contained by container?
A) 24.63 B) 43.74 C) 28.2 D) 46.75
2. In what ratio should rice at Rs.10.60 per kg be mixed with rice at Rs.12.60 per kg so that the mixture is worth Rs.11 per kg?
A) 4 : 3 B) 3 : 2 C) 2 : 3 D) 4 : 1
3. In what ratio must a grocer mix two varieties of pulses costing Rs.16 and Rs.21 per kg respectively to obtain a mixture worth Rs.18 per kg?
A) 3 : 2 B) 4 : 1 C) 5 : 4 D) 7 : 3
4. A shopkeeper has 1000 kg of rice, part of which he sells at 10% profit and the rest at 15% profit. He gains 12% on the whole. The quantity sold at 10% profit is....
A) 1200 kg B) 400 kg C) 600 kg D) 500 kg
5. How many litres of water must be added to 15 litres of milk and water containing 20% water to make it 40% water?
A) 5 litres B) 4 litres C) 3 litres D) 10 litres
6. Rs.100 was divided among 30 boys and girls such that each boy got Rs.4 and each girl got Rs.3. What is the number of boys?
A) 20 B) 15 C) 5 D) 10
7. A trader has 1500 kgs of rice. He sells a part at 15% profit and the rest at 21% profit. If he gains 19% on the whole, find the quantity sold at 15%.
A) 1200 kgs B) 500 kgs
C) 900 kgs D) 1400 kgs
8. In 16 litres of a mixture, the ratio of milk to water is 3 : 1. In order to make the ratio of milk to water as 2 : 1, the quantity of water that should be added to the mixture will be.....
A) 4 litres B) 3 litres C) 2 litres D) 6 litres
9. How many kgs of rice at Rs.10 per kg be mixed with 45 kg of rice at Rs.17 per kg to get a mixture worth Rs.13 per kg?
A) 25 kgs B) 60 kgs C) 35 kgs D) 50 kgs
10. Find the ratio in which at Rs.15.4 per kg be mixed with rice at Rs.16.30 per kg to produce a mixture worth Rs.16 per kg?
A) 2 : 3 B) 3 : 4 C) 2 : 1 D) 1 : 2
11. The cost of Type 1 material is Rs.10 per kg and Type 2 material is Rs.20 per kg. If both Type 1 and Type 2 are mixed in the ratio 3 : 2, then what is the price per kg of mixed variety of material?
A) Rs.14 B) Rs.16 C) Rs.18 D) Rs.22
12. Tea worth Rs.120 per kg and Rs.130 per kg are mixed with a third variety of tea in the ratio 1 : 1 : 3. If the mixture is worth Rs.150 per kg, what is the price per kg of the third variety of material?
Key
1-B 2-D 3-A 4-C 5-A 6-D 7-B 8-C 9-B 10-D 11-A 12-B
Explanations
Some More Questions
1. In 16 kg mixture of iron and manganese, 30% is manganese. How much iron should be added so that the proportion of manganese becomes 20%?
A) 2 kgs B) 4 kgs C) 12 kgs D) 10 kgs
2. In what ratio must tea at Rs.65 per kg be mixed with tea at Rs.74 per kg so that mixture must be worth Rs.70 per kg?
A) 2 : 3 B) 3 : 4 C) 4 : 5 D) 5 : 6
3. In what ratio must a shopkeeper mix two types of sugar costing Rs.4.60 per kg and Rs.5.80 per kg respectively so as to get a mixture worth Rs.5 per kg?
A) 2 : 1 B) 1 : 2 C) 4 : 5 D) 5 : 4
4. In what proportion must a grocer mix wheat at Rs.57 per kg and Rs.65 per kg so as to make a mixture worth Rs. 60 per kg?
A) 2 : 5 B) 5 : 3 C) 1 : 4 D) 7 : 3
5. The ratio of milk and water of four containers are 2 : 3, 3 : 2, 4 : 1, 1 : 2 respectively. In which container, is the quantity of milk relative to water minimum?
A) First B) Third C) Fourth D) Second
6. A merchant has 1000 kg of rice, one part of which he sells at 45% profit and the rest at 20% profit. He gains 35% on the whole. Find the quantity sold at 20% profit.
A) 400 kg B) 200 kg C) 500 kg D) 1000 kg
7. A trader has 48 kgs of sugar, part of which he sells at 20% profit and rest at 44% profit. He gains 33% on the whole. What is the quantity sold at 20% profit?
A) 20 kgs B) 15 kgs C) 30 kgs D) 22 kgs
8. A merchant had 100 kg of rice. He sells one part at a profit of 20% and another at 5% loss. Overall he had a gain of 10%. Find the quantity of pulses, which he had sold at 20% profit and 5% loss.
A) 60 kg, 40 kg B) 20 kg, 80 kg
C) 50 kg, 50 kg D) 30 kg, 70 kg
9. 500 g of salt solution has 20% salt in it. How much salt should be added to make it 50% in the solution?
A) 400 g B) 300 g C) 100 g D) 200 g
10. In two types of stainless steel, the ratio of Nickel and Steel are 2 : 9 and 7 : 4 respectively. In what proportion should the two types be mixed, so that the ratio of Nickel and Steel in the mixed type becomes 5 : 6?
A) 1 : 4 B) 3 : 5 C) 2 : 3 D) 7 : 2
11. In a mixture of 100l, the ratio of acid and water is 3 : 2. If the ratio of acid and water is to be 2 : 3, then the amount of water (in litres) to be added to the mixture is...
A) 25l B) 30l C) 60l D) 50l
Key
1-A 2-C 3-A 4-B 5-C 6-A 7-D 8-A 9-B 10-C 11-D
