1

ALLIGATION

ALLIGATION

2

ALLIGATION

• EXAMPLE: 1

• In what ratio must rice at Rs8.20 per kg be mixed with rice at Rs9.60 per kg, so that the mixture be worth Rs8.60 per kg?

3

ALLIGATION

• EXAMPLE:2

• How many kg of salt at Rs6.00 per kg. must a man mix with 20 kg of salt at Rs3.60 per kg. so that he may, on selling the mixture at Rs5.60 per kg, gain 40% on the outlay?

4

ALLIGATION

• EXAMPLE: 3.

• A buttler stole wine from a butt of sherry which contained 40% of spirit. He replaced what he had stolen by wine containing only 16% spirit. The butt was then 24% strength only. How much of the spirit did he steal?

5

ALLIGATION

• EXAMPLE: 4

• In what proportion must water be mixed with spirit to gain 16 2/3% by selling it at the cost price?

6

ALLIGATION

• EXAMPLE: 5

• A mixture of a certain quantity of milk with 16 litres of water is worth 90p per litre. If pure milk worth Rs1.08 per litre how much milk is there in the mixture?

7

ALLIGATION

• EXAMPLE: 6• Milk and water are mixed in a vessel A in

the proportion 5: 2, and in vessel B in the proportion 8: 5. In what proportion should quantities be taken from the two vessels so as to form a mixture in which milk and water will be in the proportion 9: 4?

8

ALLIGATION

• EXAMPLE: 7

• A goldsmith has two qualities of gold – one of 12 carats and another of 16 carats purity. In what proportion should he mix both to make an ornament of 15 carats purity?

9

ALLIGATION

• EXAMPLE: 8

• 300gm of sugar solution has 40% sugar in it. How much sugar should be added to make it 50% in the solution?

10

ALLIGATION

• EXAMPLE: 9

• There are 65 students in a class. 39rupees are distributed among them so that each boy gets 80p and each girl gets 30p. Find the number of boys and girls in the class.

11

ALLIGATION

• EXAMPLE: 10

• A person has a chemical of Rs25 per litre. In what ratio should water be mixed in that chemical so that after selling the mixture at Rs20 per litre he may get a profit of 20%?

12

ALLIGATION

• EXAMPLE: 11

• A container contained 80kg of milk. From this container 8kg of milk was taken out and replaced by water. This process was further repeated two times. How much milk is now contained by the container?

13

ALLIGATION

• EXAMPLE: 12• Nine litres are drawn from a cask full of

water and is then filled with milk. Nine litres of mixture are drawn and the cask is again filled with milk. The quantity of water now left in the cask is to that of the milk in it as 16: 9. How much does the cask hold?

14

ALLIGATION

• EXAMPL: 13

• A trader has 50 kg of pulses, part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. What is the quantity sold at 18% profit?

15

ALLIGATION

• EXAMPLE: 14• A person travels 285 km in 6 hrs in two

stages. In the first part of the journey, he travels at the speed of 40km/hr. In the second part of the journey, he travels by train at the speed of 55km/hr. How much distance did he travel by train?

16

ALLIGATION

• EXAMPLE: 15

• Mohan’s expenditure and savings are in the ratio 3: 2. His income increases by 10%. His expenditure also increases by 12%. By how many % does his saving increase?

17

ALLIGATION

• EXAMPLE: 16

• Rs1500 is invested in two such parts that if one part be invested at 6% and the other at 5%, the total interest in one year from both investments is Rs85. How much is invested at 5%?

18

ALLIGATION

• EXAMPLE:

• Sugar at Rs15 per kg is mixed with sugar at Rs20 per kg in the ratio 2: 3. Find the price per kg of the mixture.

19

ALLIGATION

• EXAMPLE:

• A man buys two cows for Rs1350 and sells one so as to lose 6% and the other so as to gain 7.5% and on the whole he neither gains nor loses. What does each cow cost?

20

ALLIGATION

21

ALLIGATION

22

ALLIGATION