Question

A shopkeeper sold \(\frac23\) 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:

• A. \( ₹24,800\)
• B. \( ₹32,600\)
• C. \( ₹37,500\)
• D. \( ₹48,000\)

Answer 1

The Correct Option is C

To determine the cost price of the whole stock of rice, let's denote the total cost price of the stock as \( C \).

1. The shopkeeper sold \( \frac{2}{3} \) of the stock at a profit of \( 5\% \):
Profit on \(\frac{2}{3}\) stock = \( \frac{2}{3} \times C \times \frac{5}{100} = \frac{C}{30} \).

2. The remaining \( \frac{1}{3} \) stock was sold at a loss of \( 2\% \):
Loss on \(\frac{1}{3}\) stock = \( \frac{1}{3} \times C \times \frac{2}{100} = \frac{C}{150} \).

3. Total profit is given as ₹ 1000:
\(\frac{C}{30} - \frac{C}{150} = 1000\)

4. Simplify the equation:
\(\frac{C}{30} - \frac{C}{150} = 1000\)
Convert to a common denominator: \(\frac{5C}{150} - \frac{C}{150} = 1000\)
\(\frac{4C}{150} = 1000\)

5. Solve for \( C \):
\(4C = 150 \times 1000\)
\(4C = 150000\)
\(C = \frac{150000}{4}\)
\(C = 37500\)

Therefore, the cost price of the whole stock of rice is ₹ 37,500.