The document discusses the concept of alligation, which is a rule that determines the ratio in which ingredients must be mixed to produce a mixture of a desired price. It provides the rule of alligation and uses it to solve example problems involving determining the mixing ratio of ingredients of different prices to produce a mixture of a specified mean price. It also provides examples involving calculating the quantity of liquid remaining after repeated removal and replacement from a container.
3. 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 of desired price.
Mean Price:
The cost of a unit quantity of the mixture is called the
mean price.
4. Rule of Alligation:
If two ingredients are mixed, then
(Quantity of cheaper / Quantity of dearer) = (C.P of dearer – mean price
/ mean price – C.P of cheaper)
5. The quantity of pure liquid= x[1-
(y/x)]^n
x--- Container’s initial volume
y--- Liters that taken out
n--- number of times we done this
operation
6. 1. In what ratio must a grocer mix two varieties of pulses
costing Rs. 15 and Rs. 20 per kg respectively so as to get
a mixture worth Rs. 16.50 kg?
A. 3:7 B. 5:7 C. 7:3 D. 7:5
7. EXPLANATIONS:
Cheaper value is 15, Dearer value is 20 & Mean value is 16.50
Required rate = 3.50 : 1.50 = 7 :3
ANSWER : C
8. 2.In what ratio must rice at Rs.9.30 kg be mixed with
rice at Rs.10.80 kg so that the mixture be worth Rs.10
kg?
A. 6:7 B. 8:7 C. 7:8 D. 7:5
10. 3. In what ratio must tea at Rs.62 per kg be mixed with
tea at rs.72 per kg so that the mixture must be worth
Rs.64.50 per kg?
A. 3:1 B. 2:1 C. 1:3 D. 1:2
11. EXPLANATIONS:
C.P of a unit quantity of 1st kind = Rs. 62
C.P of a unit quantity of 2nd kind = Rs. 72
Mean price = Rs. 64.50
ANSWER: A
12. 4.The cost of type 1 rice is Rs.15/ kg and type 2 rice is Rs.20/ kg. If both
the rice are mixed in the ratio of 2:3, then the price per kg of the mixed
variety of rice is:
A. 18 B. 20 C. 15 D. 12
13. EXPLANATIONS:
C.P of a unit quantity of 1st kind = Rs. 15
C.P of a unit quantity of 2nd kind = Rs. 20
Mean price = Rs . X
20 – X / X – 15 = 2/3
60 – 3X = 2X – 30
X = 18
ANSWER : A
14. 5. In what ratio must water be mixed with milk to
gain 20% by selling the mixture at cost price?
A. 5:1 B. 2:1 C. 1:5 D. 1:2
15.
16. EXPLANATIONS:
Water – Rs. 0
Milk – Rs. 1
Mean - Let Cost Price(C.P) of milk be Rs. 1 per litre. Then,
Selling Price(S.P) of 1 litre of mixture = Rs. 1 Gain obtained=
20% Then, C.P of 1 litre of mixture = Rs (100/120)*1 = Rs.
5/6.
ANSWER: C
17. 6. In what ratio must a Grocer mix two varieties of Tea worth
Rs.60/Kg and Rs.65/kg so that by selling the mixture at
Rs.68.20/Kg he may gain 10%?
A. 5:2 B. 2:3 C. 2:5 D. 3:2
18.
19. EXPLANATIONS:
C.P of a unit quantity of 1st kind = Rs. 60
C.P of a unit quantity of 2nd kind = Rs. 65
Mean price = Rs. 68.20 (10% GAIN)
ANSWER: D
20. 7. 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:
21. EXPLANATIONS:
Since 1st and 2nd varieties are mixed in equal proportions
So, their average price = Rs (126+135/2)= 130.50
C.P of a unit quantity of 1st kind = Rs. 130.50
C.P of a unit quantity of 2nd kind = Rs. X
Mean price = Rs. 153
ANSWER: 175.50
22. 8. A container contains 40 liters of milk, from this
container 4 liters of milk was taken out and replaced
by water. This process was repeated further two times.
How many liters of milk is now in the container?
23. EXPLANATIONS:
In Intial stage,
Milk – 40 Water – 0
Step 1:
Milk – 36 Water – 4
Step 2:
Milk – 32.4 Water – 7.6
Step – 3
Milk – 29.16 Water – 10.84
24. 9. In what ratio must water be mixed with milk to gain 16 2/3% on
selling the mixture at cost price?
A. 6:1 B. 2:1 C. 1:6 D. 1:2
26. 10. A container contains 80 liters of milk, from this container 8 liters of
milk was taken out and replaced by water. This process was repeated
further two times. How many liters of milk is now in the container?
27. EXPLANATIONS:
In Intial stage,
Milk – 80 Water – 0
Step 1:
Milk – 72 Water – 8
Step 2:
Milk – 64.8 Water – 15.2
Step – 3
Milk – 58.32 Water – 21.68
