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ALLEGATION
Allegation is used in different types of sums where two different situations of the same unit are catenated. Suppose two different situations say two items of different prices per unit weight are mixed to form a resultant whose price is given. Then after performing the allegation we will get a ratio which is the proportion of weight.
In general, if the unit is given as Unit A/Unit B or Unit A per Unit B, then the ratio obtained after the allegation is based on Unit B only.
Here some sums have been provided with solutions. You will be able to grab the concept easily if you follow some solutions in the beginning. Then it is suggested to go solve without seeing any solution.
Exercise A
1. In what proportion must wheat at Rs. 3.40 per kg be mixed with wheat at Rs. 3.90 per kg, so that the mixture is worth Rs. 3.55 a kg?
a) 3 : 5
b) 7 : 3
c) 1 : 3
d) 3 : 1
2. In what proportion must tea at Rs. 13 per kg be mixed with tea at Rs. 17 per kg, so that the mixture is worth Rs. 16 a kg?
a) 1 : 1
b) 1 : 3
c) 2 : 3
d) 3 : 1
3. In what proportion must coffee at Rs. 23 per kg be mixed with coffee at Rs. 30 per kg, so that the mixture be worth Rs 27 a kg?
a) 4 : 3
b) 4: 5
c) 5 : 4
d) 3 : 4
4. In what proportion must cotton at Rs. 23.50 per kg be mixed with cotton at Rs. 29.50 per kg, so that the mixture is worth Rs. 25 a kg?
a) 3 : 1
b) 1 : 3
c) 3 : 2
d) 2 : 3
5. In what proportion must sugar at Rs. 14.60 a kg be mixed with sugar at Rs. 14.45 a kg so that the mixture may be worth Rs. 14.54 a kg?
a) 2 : 1
b) 2 : 3
c) 3 : 2
d) 4 : 1
6. In what proportion must tea at Rs. 49.50 per kg be mixed with tea at Rs. 52.50 per kg to produce a mixture worth Rs. 50.50 kg?
a) 2 : 1
b) 1 : 2
c) 4 : 1
d) 3 : 2
7. In what proportion must a brewer mix beer at Rs. 13 a litre with bear at Rs. 8 a litre, so that the mixture may be worth Rs. 10 a litre?
a) 2 : 1
b) 1 : 2
c) 3 : 2
d) 2 : 3
8. How must a grocer mix teas at Rs 4 a kg and Rs 4.50 a kg so that the mixture may be worth Rs 4.20 a kg?
a) 2 : 3
b) 3 : 2
c) 3 : 1
d) 1 : 3
9. In what ratio should gold at Rs 18 per gm be mixed with gold at Rs 13 per gm so that the resulting mixture be worth Rs 16 per gm.
a) 3 : 2
b) 3 : 1
c) 1 : 1
d) 2 : 3
10. In what ratio must a grocer mix sugar at 74 paise per kg with sugar at 50 paise per kg so that by selling the mixture at 63 paise per kg he may gain 1/8 of his outlay?
a) 1 : 3
b) 3 : 1
c) 2 : 3
d) 3 : 2
11. Sugar at Rs 10 per kg is mixed with sugar at Rs 15 per kg in the ratio 2 : 3. Find the price per kg of the mixture.
a) 10
b) Rs 11
c) Rs 12
d) Rs 13
12. A grocer buys black tea at Rs 6.25 per kg and green tea at Rs 8.50 per kg. How must he mix them so that by selling the mixture at Rs 8 per kg he may gain 1/7 of his outlay?
a) 1 : 2
b) 1 : 3
c) 2 : 1
d) 3 : 1
13. In what proportion should water be mixed to wine at Rs 20 a litre to reduce the price to Rs 16 a litre?
a) 1 : 4
b) 4 : 1
c) 2 : 3
d) 3 : 2
14. Currants at Rs 51 per kg are mixed with currants at Rs 91 per kg to make a mixture of 17 kg worth Rs 71 per kg, how many kilograms of each are taken?
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15. A person bought 60 quintals of rice of two different sorts for Rs 4642.50. The better sort costs Rs 80 per quintal and the worse Rs 75.50 per quintal. How many quintals were there for each sort?
a) 25 quintals, 35 quintals
b) 20 quintals, 40 quintals
c) 32 quintals, 28 quintals
d) None of these
16. A man has whiskey worth Rs 23 a litre and another lot worth Rs 17 a litre. Equal quantities of these are mixed with water to obtain a mixture of 50 litres worth Rs 16 a litre. Find how much water the mixture contains?
a) 5 litres
b) 10 litres
c) 15 litres
d) 20 litres
Exercise B
1. Jaydeep purchased 25 kg of rice at the rate of Rs 16.50 per kg and 35 kg of rice at the rate of Rs 25.50 per kg. He mixed the two and sold the mixture. Approximately, at what price per kg did he sell the mixture to make 25 per cent profit?
a) Rs 26.50
b) Rs 27.50
c) Rs 28.50
d) Rs 30.00
2. Jagtap purchases 30 kg of wheat at the rate of Rs 11.50 per kg and 20 kg of wheat at the rate of Rs 14.25 per kg. He mixed the two and sold the mixture. Approximately at what price per kg should he sell the mixture to make 30 per cent profit?
a) Rs 16.30
b) Rs 18.20
c) Rs 15.60
d) Rs 14.80
3. Prabhu purchased 30 kg of rice at the rate of Rs 17.50 per kg and another 30 kg of rice at a certain rate. He mixed the two and sold the entire quantity at the rate of Rs 18.60 per kg and made a 20 per cent overall profit. All that price per kg did he purchase a lot of another 30 kg rice?
a) Rs 14.50
b) Rs 12.50
c) Rs 15.50
d) Rs 13.50
4. A grocer purchased 20 kg of rice at the rate of Rs 15 per kg and 30 kg of rice at the rate of Rs 13 per kg.
a) Rs 28.00
b) Rs 20.00
c) Rs 18.40
d) Rs 17.40
5. A grocer buys two kinds of barley at Re 1.50 P and 95 paise per kilogram respectively. In what proportion should these be mixed so that by selling the mixture at Re 1.60 P per kilogram, 25 % may be gained?
a) 3 : 1
b) 3 : 2
c) 4 : 1
d) 2 : 3
6. In what proportion must a grocer mix one kind of wheat at Rs 4.50 per kg with another Rs 4 per kg in order that by selling the mixture at Rs 5.20 per kg he may make a profit of 20 per cent?
a) 3 : 1
b) 4 : 1
c) 3 : 2
d) 2 : 1
7. How many kg of salt costing 40 P per kg must be mixed with 16 kg of salt costing 55 P per kg so that 25 per cent may be gained by selling the mixture at 60 P per kg?
a) 14 kg
b) 16 kg
c) 12 kg
d) 15 kg
8. What weight of wheat worth Rs 4.20 per kg should be mixed with 60 kg of sugar worth Rs 2.70 per kg so that when the mixture is sold at Rs 3.30 per kg, there may be neither gain nor loss.
a) 50 kg
b) 45 kg
c) 55 kg
d) 40 kg
9. Kantilal mixes 80 kg of sugar worth Rs 6.75 per kg with 120 kg worth of Rs 8 per kg. At what rate shall he sell the mixture to gain 20 %? (SBI PO Exam 1987)
a) Rs 7.50
b) Rs 9
c) Rs 8.20
d) Rs 8.85
