Mukesh purchased 40 kg of wheat at 12.50 per kg and 25 kg of wheat at 15.10 per kg. He mixed the two qualities of wheat for selling. At what rate should it be sold to gain 10%?

Options

A. 13.25
B. 13.5
C. 14.75
D. 14.85

Answer

To find the selling price at which Mukesh should sell the mixed wheat to gain a profit of 10%, we first need to calculate the total cost price of the wheat he purchased and then determine the selling price based on the desired profit percentage.

### Step-by-Step Solution:

1. **Calculate the cost of the first quantity of wheat:**
- Mukesh purchased 40 kg of wheat at ₹12.50 per kg.
- Cost Price (CP) for the first quantity = Quantity × Price per kg
- CP = 40 kg × ₹12.50/kg = ₹500

2. **Calculate the cost of the second quantity of wheat:**
- Mukesh purchased 25 kg of wheat at ₹15.10 per kg.
- Cost Price (CP) for the second quantity = Quantity × Price per kg
- CP = 25 kg × ₹15.10/kg = ₹377.50

3. **Calculate the total cost price of the mixed wheat:**
- Total CP = CP of first quantity + CP of second quantity
- Total CP = ₹500 + ₹377.50 = ₹877.50

4. **Calculate the total quantity of wheat:**
- Total Quantity = Quantity of first wheat + Quantity of second wheat
- Total Quantity = 40 kg + 25 kg = 65 kg

5. **Calculate the desired selling price for a 10% gain:**
- To gain 10%, Mukesh needs to sell at a price that is 110% of the total cost price.
- Selling Price (SP) = Total CP × (1 + Gain Percentage)
- SP = ₹877.50 × (1 + 0.10) = ₹877.50 × 1.10 = ₹965.25

6. **Calculate the selling price per kg:**
- Selling Price per kg = Total SP / Total Quantity
- Selling Price per kg = ₹965.25 / 65 kg = ₹14.85

### Final Answer:
Mukesh should sell the wheat at ₹14.85 per kg to gain a profit of 10%.

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