Alligation & Mixture
ALLIGATION OR MIXTURE
Alligation : It is the rule that enables us to find the ratio in which two or more
ingredients at the given price must be mixed to produce a mixture at a desired rate
Mean Price: The cost price of a unit quantity of the mixture is called the mean price.
Rule of Alligation: Let the two ingredients be mixed. Then
C.P of 1 units of cheaper(c) C.P of 1 unit of dearer(d)
Mean Price (m)
(d–m) (m–c)
Cheaper
Quantity: Dearer Quantity = ( d – m ) : ( m – c )
Rule of Mixture: From a container having x units of a liquid, suppose y units are
taken out and replace by water.
y
n
After n operations, quantity of pure liquid = x1 − units
x
Exercise 1
1. In what ratio must rice at Rs.30 per kg mixed with rice at Rs.10.80 per kg so
that the mixture be worth Rs.10per kg `
A. 7:8 B.8:7 C. 5:7 D. 7:5
2. In what ratio must wheat at Rs.3.20 pe rkg be mixed with wheat at Rs.2.90 per
kg so that the mixture be worth Rs.3.08 per kg
A. 3:2 B. 2:3 C. 3:1 D. 1:3
3. How many kilograms of sugar costing Rs/.9 per kg must be mixed with 27kg
of sugar costing Rs.7 per kg so that there may ba gain of 10% by selling the
mixture at Rs.9.24 per kg ?
A. 66 kg B. 64 kg C. 63 kg D.61 kg
4. In what ratio must water be mixed with milk to gain 16 2/3% on selling the
mixture at cost price ?
A. 1:5 B. 1:6 C. 2:5 D.5:1
5. Two vessels A and B contain milk and water mixed in the ratio 8:5 and 5:2
res. The ratio in which these two mixtures be mixed to get a new mixture
containing milk and a water in the ratio 9:4?
A. 5:2 B. 2:7 C. 7:2 D. 5:7
6. In what ratio water be mixed with milk costing Rs.12 per liter to obtain a
mixture worth of Rs.8 per litre?
A. 1:2 B. 3:1 C. 2:1 D.1:3
7. A sum of Rs.4000 is lent out in two parts, one at 8% simple interest and the
other at 10% simple interest. In the annual interest is Rs.352, the sum lent at
8% is
A. 2600 B. 2500 C. 2400 D.2300
8. A merchant has 100kg of sugar, part of which he sells at 8% profit and the rest
at 18% profit. He gains 14% on the whole. The quantity sold at 18% profit is
A. 60 kg B. 600 kg C. 400 kg D.500 kg
9. Two vessels A and B contain milk and water mixed in the ratio 4:3 and 2:3 in
what ratio must these mixtures be mixed to form new mixture containing half
milk and half water?
A. 5:7 B. 2:7 C. 6:5 D.7:5
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Alligation & Mixture
10. A jar full of whisky contains 40% alcohol. A part of this whisky is replaced
by another containing 19% alcohol and now the percentage of alcohol was
found to be 26% the quantity of whisky replaced is
A. 3/2 B. 2/3 C. 3/4 D. 4/3
11. 729ml of mixture contains milk and water in the ratio 7:2 how much more
wate is to be added to get a new mixture containing milk and water in the ratio
7:3?
A. 80 ml B. 75 ml C. 79 ml D. 81 ml
12. A sum of Rs.312 was divided amng 100boys and girls in such a way that the
boy gets Rs.3.60 and each girl Rs.2.40 the number of girls is
A. 30 B. 35 C. 40 D. 45
13. A man covered a distance of 2000km in 18 hours partly by bus at 72kmph and
partly by train at 16kmph the distance covered by bus is
A. 700 km B. 680 km C. 720 km D. 705 km
14. A sum of rs.36.90 is made up of 180 coins which are either 10 paise coins or
25 p coins. The number of 10 p coins is
A. 61 B. 52 C. 45 D. 54
15. A dishonest milk man professes to sell his milk at cost price but he mixed it
with water and thereby gains 25%. The percentage of water in the mixture is
A. 10% B. 20% C. 25% D. 35%
16. A mixture of 20kg of spirt and water contains 10 water How much water must
be added to this mixture to raise the percentage of water to 25%?
A. 3 kg B. 2 kg C. 1 kg D. 4 kg
17. A container contains 40kg of milk, from this container 4kg 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?
A. 29.16 kg B. 29.59 kg C. 30.19 kg D.30.16 kg
18. A can contains a mixture of two liquids A and B in the ratio 7:5 when 9 litres
of mixture are drawn off and the can is filled with B, the ratio of A and B
becomes 7:9 how many litres of liquids A was contained by the can initially?
A. 27 B. 25 C. 23 D. 21
19. Two vessels A and B contain milk and water mixed in the ratio 5:2 and 8:5
respectively. Find the ratio in which these mixtures are to be mixed to get a
new mixture containing milk and water in the ratio 9:4
A. 7:2 B. 2:7 C. 5:7 D. 7:5
20. How many kg of rice costing Rs. 18.30 per kg must be mixed with 126 kg of
rice costing Rs.8.55 per kg so that 20% may be gained by selling the mixture
at Rs.14.40 per kg.
A. 69 kg B. 44 kg C. 86 kg D. None
Exercise 2
1. The ratio in which the price at Rs. 7.20 a kg be mixed with rice at Rs.5.70
a kg to produce a mixture worth Rs.6.30 a kg, is
A. 2:3 B. 4:1 C. 2:1 D. None
2. In what ratio must a grocer mix teas worth Rs.60 a kg and Rs.65 a kg so
that by selling the mixture at Rs. 68.20 a kg, he may gain 10%
A. 3:4 B. 1:3 C. 3:2 D. None
3. Milk and water in two vessels A and B are in the ratio 4:3 and 2:3
respectively. In what ratio the liquids in both the vessels should be mixed
to obtain a new mixture in vessels containing half milk and half water
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Alligation & Mixture
A.4:5 B. 2:5 C. 2:3 D. 7:5
4. A merchant has 1000 kg of sugar, part of which he sells at 8% profit and
the rest at 18% profit. He gains 14% on the whole. The quantity sold at 8%
profit is
A. 500 kg B. 400 kg C. 350 kg D. None
5. A milk vendor has 2 cans of milk. The first contains 25% water and the
rest milk. The second contains 50% water. How much milk should he mix
from each of the containers so as to get 12 liters of milk such that the ratio
of water to milk is 3:5 ?
A. 4 lit, 8 lit B. 6 lit, 6 lit C. 5 lit. 7 lit D.7 lit,5 lit
6. A vessel contains 56 litre of mixture of milk and the water in the ratio 5:2.
how much water should be mixed with it so that the ratio of milk to water
to 4:5
A. 34 lit B. 56 lit C. 12 lit D. None
7. In a mixture of 60 litres, the ratio of milk and water is 2:1. if the ratio of
milk and water is to be 1:2, then the amount of water to be further added is
A. 50 lit B. 60 lit C. 38 lit D. None
8. A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup.
How much of the mixture must be drawn off and replaced with water so
that the mixture may be half water and half syrup.
A. 1/3 B. 1/4 C. 1/5 D. 1/7
9. A merchant has 1000 kg of sugar, part of which he sells at 8% profit and
the rest at 18% profit. He gains 14% on the whole. The quantity sold at 8%
profit is
A. 500 kg B. 400 kg C. 350 kg D. None
10. A discount milk man professes to sell his milk at cost price but he mixes it
with water and thereby gains 25%. The percentage of water in the mixture
is:
A. 4% B. 6 ¼ % C. 20% D. 25%
