**SSC CHSL Topic Wise Study Material – Quantitative Aptitude – Alligation and Mixture**

Contents

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Alligation literally means ‘linking’. It is a rule to find

(a) the ratio in which two or more ingredients at their respective prices should be mixed to give a mixture at a given price.

(b) The mean or average price of a mixture when the prices of two or more ingredients which may be mixed together and the proportion in which they are mixed are given.

**Rules of Mixture**

There are some important rules related to mixture which are given below.

**Rule I** If the ingredients are mixed in a ratio, then according to the rule of mixture,

or

**Note** Here, the value of the mixture is always higher than the lowest value and lower than the highest value of the items being mixed. Hence, quantity of cheaper: quantity of dearer (d – m): (m – c)

**Example Two solutions of 90% and 97% purity are mixed, resulting in 21 L of mixture of 94% purity. The quantity of the second solution in the resulting mixture in litres, is ssc (10+2) 2010**

(a) 15

(b) 12

(c) 9

(d) 6

**Example Alcohol and water in two vessels A and B are in the ratio 5: 3 and 5: 4, respectively. In what ratio, the liquids in both the vessels be mixed to obtain a new mixture in vessel C in the ratio 7: 5? ssc (10+2) 2010**

(a) 2:3

(b) 3:2

(c) 3:5

(d) 2:5

**Rule II** Let the ratio of milk to water in a mixture be a : b, if x L of water is added to the mixture, then the ratio of milk to water becomes a: c. Then, the quantity of milk in a mixtures is ax/c-a L and that of water in mixture is bx/c-b L.

**Example Milk and water are in the ratio of 3 : 2, in a mixture of 80 L. How much water should be added so that the ratio of the milk and water becomes 2 : 3?**

(a) 25 L

(b) 40 L

(c) 35 L

(d) 20 L

**Reference Corner**

**1. One type of liquid contains 20% water and the second type of liquid contains 35% of water. A glass is filled with 10 parts of first liquid and 4 parts of second liquid. The water in the new mixture in the glass is SSC (10 + 2) 2013**

(a)12 1/7%

(b)24 2/7%

(c)37%

(d)46%

**Answer:**

**2. Zinc and copper are in the ratio 5 : 3 in 400 g of an alloy. How much of copper (in g) should be added to make the ratio 5:4? SSC (10+2)2013**

(a) 72

(b) 200

(c) 50

(d) 66

**Answer:**

**3. In two blends of mixed tea, the ratios of Darjeeling and Assam tea are 4 : 7 and 2:5. The ratio in which these two blends should be mixed to get the ratio of Darjeeling and Assam tea in the new mixture as 6: 13 is SSC (10+2) 2013**

(a) 2:7

(b) 5:13

(c) 4:13

(d) 22:35

**Answer:**

(d)

**Practice Exercise**

**1. By mixing two different quantities of pulses in the ratio 2:3 and selling the mixture at the rate of Rs 22/kg a shopkeeper makes a profit of 10%. If the cost of the smaller quantity be Rs 14/kg, then the cost per kg of the larger quantity is**

(a)Rs 23

(b)Rs 24

(c)Rs 25

(d) None of these

**2. A drum contain 20 L of a paint. From this 2 L of paint is taken out and replaced by 2 L of oil. Again 2 L of this mixture is replaced by 2 L of oil. If the operation is performed once again, then final ratio of the paint and the oil in the drum would be ?**

(a)729:271

(b)172:279

(c)3:7

(d)217: 972

**3. Several litres of acid were drawn off a 54 L vessel full of acid and an equal amount of water added. Again the same volume of the mixture was drawn off and replaced by water. As a result, the vessel contained 24 L of pure acid. How much of the acid was draw off initially?**

(a) 12 L

(b) 16 L

(c) 18 L

(d) 24 L

**4. There are three containers of equal capacity. The ratio of sulphuric acid to water in the first container is 3 : 2, that in the second container is 7 : 3 and in the third container 11:4. If all the liquids are mixed together, then the ratio of sulphuric acid to water in the mixture will be**

(a)61:29

(b)61:28

(c)60 :29

(d)59 :29

**5. A container is filled with liquid, 6 part of which are water and 10 part milk. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half milk?**

(a) 1/3

(b) 1/7

(c) 1/5

(d) 1/8

**6. A man buys milk at a certain price per litre and after mixing it with water sells it again at the same price. How many mL of water does he mix in every litre of milk if he makes a profit of 25%?**

(a) 250 mL

(b) 200 mL

(c) 150 mL

(d) 30 mL

**7. A barrel contains a mixture of wine and water in the ratio 3 :1. How much fraction of the mixture must be drawn off and substituted by water so that the ratio of wine and water in the resultant mixture in the barrel become 1:1?**

(a) 1/4

(b) 1/3

(c) 1/2

(d) 2/3

**8. Atul bought 30 kg of rice at Rs 8.50/kg and 20 kg of rice at Rs 8.00/kg. If he has to make a 20% profit, at approximately, what rate per kg should he sell the rice?**

(a) Rs 10.00

(b) Rs 12.00

(c) Rs 8.50

(d) Rs 8.00

**9. Raghav buys milk at a certain price and after mixing it with water sells it again at the same price. How many mile litres of water he mixes in a liters of milk, if he makes a profit of 20%?**

(a) 200 mL

(b) 250 mL

(c) 150 mL

(d) 20 mL

**10. Pure ghee costs Rs 100/kg. After adulterating it with vegetable oil costing Rs 50/kg. A shopkeeper sells the mixture at Rs 96/kg, thereby making a profit of 20%. In what ratio does he mix the two?**

(a) 1:2

(b) 3:2

(c) 3:1

(d) 2:3

**11. Two types of oils having the rates of Rs 4/kg and Rs 5/kg respectively are mixed in order to produce a mixture having the rate of Rs 4.60/kg. What should be the amount of the second type of oil if the amount of the first type of oil in the mixture is 40 kg?**

(a) 75 kg

(b) 50 kg

(c) 60 kg

(d) 40 kg

**12. 400 students took a mock exam in Delhi 60% of the boys and 80% of the girls cleared the cut off in the examination. If the total percentage of students qualifying is 65%, how many girls appeared in the examination?**

(a) 100

(b) 120

(c) 150

(d) 300

**13. A cistern contains 50 L of water. 5 L of water is taken out of it and replaced by wine. The process in repeated again. Find the proportion of wine and water in the resulting mixture.**

(a) 1:4

(b) 41:50

(c) 19:81

(d) 81:19

**14. A dishonest grocer professes to sell pure butter at cost price, but he mixes it with adulterated fat and thereby gain 25%. Find the percentage of adulterated fat in the mixture assuming that adulterated fat is freely available.**

(a) 20%

(b) 25%

(c) 33.33%

(d) 40%

**15. 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. The price of the third variety per kg will be SSC (10+2) 2012**

(a) Rs 169.5

(b) Rs 170.0

(c) Rs 175.5

(d) Rs 180.0

**16. A and B are two alloys of gold and copper in the ratio 7: 2 and 7:11 respectively. If equal quantities of these two alloys are melted to form a new alloy C, then the ratio of gold and copper in C is. SSC (10+2) 2012 **

(a) 6:5

(b) 9:4

(c) 12:7

(d) 7:5

**17. A can contain a mixture of two liquids A and B in the ratio 7 : 5. When 9L of mixture is drain off and the can is filled with B, the ratio of A and B becomes 7 : 9. How many litres of liquid A was contained by the can initially? SSC (10+2) 2012**

(a) 10

(b) 20

(c) 21

(d) 25

**18. Two vessels A and B contain milk and water mixed in the ratio 8: 5 and 5:2, respectively. The ratio in which these two mixtures be mixed to get a new mixture containing 69 3/13 % milk is SSC (10 + 2) 2012**

(a)2:7

(b)3:5

(c)5:2

(d)5:7

**19. A mixture of milk and water is such that the quantity of milk is 3/5 that of water. The proportion of milk in the mixture is SSC (10+2) 2011**

(a) 1/8

(b) 1/2

(c) 3/8

(d) 5/8

**20. Acid and water are mixed in a vessel A in the ratio of 5:2 and in the vessel B in the ratio of 8 : 5. In what proportion should quantities be taken out from the two vessels so as to form a mixture in which the acid and water will be in the ratio of 9 : 4? SSC (10+2) 2011**

(a) 7 :2

(b) 2:7

(c) 7 : 4

(d) 2 :3

**Answers**

**Hints & Solutions**

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