Allegations and Mixtures
Concepts
Examples
How To Solve Allegations
Suppose the average weight of a group of objects O1 is A1 and average weight of group of objects O2 is
A2 and A1 < A2, then we can write the data in the manner as shown in the figure. (Aw−A2)
: (Aw−A1) gives the ratio of O1 : O2.
Allegations does not give the actual volume to be mixed but only the ratio in which volumes are to be mixed.
Question 1 A shopkeeper sells two types of rice A and B. If he sold 30% of type A rice at a profit of 50% and sold 90% of the rice of type B at a profit of 10%. What is the averge profit percent of the shopkeeper, if he sells only these two types of rice.
| 35% | 45% |
| 40% | 55% |
C
Since the profit on rice of type B = 10% ∴ A1 = 10 Since the profit on rice of type A = 50% ∴ A2 = 50
Let the average profit be Rs x ∴ Aw = x
$\frac{50-x}{x-10}=\frac{3}{1}\Rightarrow50-x=3x-30$50−xx−10 =31 ⇒50−x=3x−30
⇒ x = 20
∴ Average profit of the shopkeeper is 40%
Question 2 How much water should be mixed with 6L pure milk to make the concentration of milk 60%.
| 4L | 2L |
| 3L | 5L |
A
Since the concentration of milk in water = 0 ∴ A1 = 0 Since the concentration of pure milk = 100 ∴ A2 = 100
Since the concentration of milk in milk-water solution = 60 ∴ Aw = 60
∴ Ratio in which water and milk should be added = 2:3
∴ Volume of water to be mixed = 4L
Question 3 A dealer buys 11 kg of wheat at Rs 275 and mixes it with another quantity of wheat in the ratio of 4:5. The price of the resulting mixture is Rs 30 per kg. Finf the price of this other quantity of wheat.
| Rs 37 per kg | Rs 31 per kg |
| Rs 24 per kg | Rs 34 per kg |
D
Price per kg of wheat = $\frac{275}{11}=25$27511 =25 Rs Since the of wheat = Rs 25 ∴ A1 = 25
Let the price of rice of other type be Rs x ∴ A2 = x
The average price of wheat = Rs 30 ∴ Aw = 30
∴$\frac{5}{x-30}=\frac{5}{4}\Rightarrow20=5x-150$5x−30 =54 ⇒20=5x−150
⇒ x = 34
∴ Price of wheat of other type = Rs 34 per kg
Question 4 If the average weight of a class of 60 students is 50 and the average weight of a class of 40 students is 45 , then what will be the average weight of both the classes combined.
| 24 | 26 |
| 45 | 48 |
D
Since the average weight of class of 40 students = 45 ∴ A1 = 45 Since the average weight of class of 60 students = 50 ∴ A2 = 50
Let the average weight of both the classes combined be x kg.
O1:O2 = 40:60 = 2:3
$\frac{50-x}{x-45}=\frac{2}{3}$50−xx−45 =23
$150-3x=2x-90$150−3x=2x−90
$x=48$x=48
∴ Average weight of both the classes combined = 48 kg
Question 5 A person travels at a speed of 25 km/hr for 30min and then travels at 40km/hr for next 20 min to reach his destination. Find his average speed in the whole journey.
| 21 km/hr | 31 km/hr |
| 33 km/hr | None of these |
B
Since the person travels for 30 min at speed of 25 km/hr ∴ A1 = 25 Since the person travels for 20 min at speed of 40 km/hr ∴ A2 = 40
Let the average speed of the person be x km/hr ∴ Aw = 500
$\frac{40-x}{x-25}=\frac{3}{2}\Rightarrow80-2x=3x-75$40−xx−25 =32 ⇒80−2x=3x−75
⇒ x = 31
∴ Average speed of the person in the whole journey was 31 Km/hr
Question 6 In what ratio should a 65% milk solution and 85% milk solution should be mixed so that the new solution is a 80% milk solution.
| 1:2 | 1:3 |
| 1:4 | 2:3 |
B
Since the concentration of milk in water = 65 ∴ A1 = 65 Since the concentration of pure milk = 85 ∴ A2 = 85
Since the concentration of milk in milk-water solution = 80 ∴ Aw = 80
∴ Ratio in which the two solutions should be mixed = 1:3
Allegations and Mixtures
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