A shopkeeper sold 2/3 of his stock of rice at a profit of 5% and the remaining stock at a loss of 2%. If his total profit was ₹1000, then the cost price of the whole stock of rice is:

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Accepted Answer

#### Step 1: Let the Cost Price of the Whole Stock Be $$ x $$
- Profit from **2/3** of the stock:  
  $$ 	ext{Profit} = \frac{2}{3} \cdot x \cdot 5\% = \frac{2}{3} \cdot x \cdot \frac{5}{100} = \frac{10x}{300}. $$

- Loss from **1/3** of the stock:  
  $$ 	ext{Loss} = \frac{1}{3} \cdot x \cdot 2\% = \frac{1}{3} \cdot x \cdot \frac{2}{100} = -\frac{2x}{300}. $$

#### Step 2: Total Profit Equation
The total profit is given as ₹1000. Combine the profit and loss:  
$$
	ext{Total Profit} = \frac{10x}{300} - \frac{2x}{300}.
$$

Simplify:  
$$
	ext{Total Profit} = \frac{8x}{300}.
$$

Equating to ₹1000:  
$$
\frac{8x}{300} = 1000.
$$

#### Step 3: Solve for $$ x $$
Multiply through by 300:  
$$
8x = 300000.
$$

Divide by 8:  
$$
x = 37500.
$$

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#### Final Answer:
The cost price of the whole stock is **₹37,500**, making Option **(c)** correct.

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