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 ∴ A_w = 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%

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 ∴ A_w = 60

∴ Ratio in which water and milk should be added = 2:3

∴ Volume of water to be mixed = 4L

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 ∴ A_w = 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

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

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 ∴ A_w = 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

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 ∴ A_w = 80

∴ Ratio in which the two solutions should be mixed = 1:3