14 A grocer buys 160 kg of rice at ? 27 per kg and mixes it with 240 kg of rice available at ? 32 per kg. At what rate per kg should he sell the mixture to gain 20% on the whole?

Answer

To solve the problem step by step, we will calculate the cost price of the mixture first, and then determine the selling price required to achieve a 20% profit.

### Step 1: Calculate the total cost of each variety of rice.

1. **Cost of the first variety (160 kg at ₹27 per kg):**
\[ \text{Cost}_1 = 160 \, \text{kg} \times 27 \, \text{₹/kg} = 4320 \, \text{₹} \]

2. **Cost of the second variety (240 kg at ₹32 per kg):**
\[ \text{Cost}_2 = 240 \, \text{kg} \times 32 \, \text{₹/kg} = 7680 \, \text{₹} \]

### Step 2: Calculate the total cost of the mixture.

\[ \text{Total Cost} = \text{Cost}_1 + \text{Cost}_2 = 4320 \, \text{₹} + 7680 \, \text{₹} = 12000 \, \text{₹} \]

### Step 3: Calculate the total weight of the mixture.

\[ \text{Total Weight} = 160 \, \text{kg} + 240 \, \text{kg} = 400 \, \text{kg} \]

### Step 4: Calculate the cost price (CP) per kg of the mixture.

\[ \text{CP per kg} = \frac{\text{Total Cost}}{\text{Total Weight}} = \frac{12000 \, \text{₹}}{400 \, \text{kg}} = 30 \, \text{₹/kg} \]

### Step 5: Calculate the selling price (SP) to gain a 20% profit.

1. **Calculate the profit percentage:**
\[ \text{Profit} = 20\% \text{ of CP} = 0.20 \times 30 \, \text{₹} = 6 \, \text{₹} \]

2. **Calculate the selling price:**
\[ \text{SP} = \text{CP} + \text{Profit} = 30 \, \text{₹} + 6 \, \text{₹} = 36 \, \text{₹/kg} \]

### Final Answer:
The selling price per kg of the mixture should be **₹36** to gain a 20% profit.

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