A shopkeeper mixes two type of sugar i.e: 45 kg of Rs.42 per kg and 75 kg of Rs 50 per kg. Find at what price he has to sell the mixture to get 10% profit?

Options

A. A)52.8 Rs/kg
B. B)51.7 Rs/kg
C. C)50.7Rs/kg
D. D)53 Rs/kg

Answer

To solve the problem, we need to find the cost price of the mixture of two types of sugar and then calculate the selling price to achieve a 10% profit. Here’s a step-by-step breakdown:

### Step 1: Calculate the total cost of each type of sugar.
- For the first type of sugar:
- Weight = 45 kg
- Price per kg = Rs. 42
- Total cost = Weight × Price per kg = 45 kg × Rs. 42/kg = Rs. 1890

- For the second type of sugar:
- Weight = 75 kg
- Price per kg = Rs. 50
- Total cost = Weight × Price per kg = 75 kg × Rs. 50/kg = Rs. 3750

### Step 2: Calculate the total weight of the mixture.
- Total weight = Weight of first type + Weight of second type = 45 kg + 75 kg = 120 kg

### Step 3: Calculate the total cost of the mixture.
- Total cost of mixture = Cost of first type + Cost of second type = Rs. 1890 + Rs. 3750 = Rs. 5640

### Step 4: Calculate the cost price (CP) per kg of the mixture.
- Cost price per kg = Total cost of mixture / Total weight = Rs. 5640 / 120 kg = Rs. 47

### Step 5: Calculate the selling price (SP) to achieve a 10% profit.
- Profit = 10% of CP = 10/100 × Rs. 47 = Rs. 4.7
- Selling Price = Cost Price + Profit = Rs. 47 + Rs. 4.7 = Rs. 51.7

### Conclusion:
The shopkeeper has to sell the mixture at Rs. 51.7 per kg to achieve a 10% profit.

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