A shopkeeper has 12 kg of pure rice and 4 kg of impure rice. He mixes both type of rice but 4 kg of the mixture gets spoiled. If he again mixes 4 kg of impure rice to the remaining mixture and professes to sell mixture at a profit of 20% on cost of pure rice. Then what is actual profit or loss percentage if cost of impure rice is 40% of cost of pure rice.

Options

A. `(400)/(19)%`
B. `(250)/(21)%`
C. `(250)/(19)%`
D. `(500)/(19)%`

Answer

To solve the problem step by step, let's break it down systematically.

### Step 1: Calculate the initial quantities of rice
The shopkeeper has:
- 12 kg of pure rice
- 4 kg of impure rice

### Step 2: Calculate the total quantity of the mixture before spoilage
Total mixture = Pure rice + Impure rice
= 12 kg + 4 kg
= 16 kg

### Step 3: Account for the spoiled rice
The shopkeeper loses 4 kg of the mixture due to spoilage.
Remaining mixture = Total mixture - Spoiled rice
= 16 kg - 4 kg
= 12 kg

### Step 4: Determine the new mixture after adding more impure rice
The shopkeeper adds 4 kg of impure rice to the remaining mixture.
New total mixture = Remaining mixture + Added impure rice
= 12 kg + 4 kg
= 16 kg

### Step 5: Calculate the cost price of pure and impure rice
Let the cost price of pure rice be \( C \).
Then, the cost price of impure rice is 40% of \( C \), which is \( 0.4C \).

### Step 6: Calculate the total cost price of the rice
Total cost price = (Cost of pure rice) + (Cost of impure rice)
- Cost of pure rice = 12 kg × \( C \) = \( 12C \)
- Cost of impure rice = 4 kg × \( 0.4C \) = \( 1.6C \)

Total cost price = \( 12C + 1.6C = 13.6C \)

### Step 7: Calculate the selling price of the mixture
The shopkeeper sells the mixture at a profit of 20% on the cost of pure rice.
Selling price = Cost price of pure rice + Profit
= \( 12C + 0.2 \times 12C = 12C + 2.4C = 14.4C \)

### Step 8: Calculate the total selling price of the entire mixture
Since the total mixture is 16 kg, we need to find the selling price per kg.
Selling price per kg = \( \frac{14.4C}{16} = 0.9C \)

Total selling price for the 16 kg mixture = 16 kg × \( 0.9C = 14.4C \)

### Step 9: Calculate profit or loss
Profit = Selling Price - Cost Price
= \( 14.4C - 13.6C = 0.8C \)

### Step 10: Calculate profit percentage
Profit percentage = \( \frac{\text{Profit}}{\text{Cost Price}} \times 100 \)
= \( \frac{0.8C}{13.6C} \times 100 \)
= \( \frac{0.8}{13.6} \times 100 \)
= \( \frac{80}{13.6} \approx 5.88\% \)

### Final Answer
The actual profit percentage is approximately **5.88%**.