Question

A shopkeeper sells two items at Rs. 1000 each. On one, he gains 25, and on the other, he loses 20. What is his overall profit or loss percentage?

• A. 2.5 loss
• B. 2.5 profit
• C. No profit, no loss
• D. 5 loss

Hint:

For profit and loss on multiple items, calculate individual CPs using SP and percentage, then find total CP, SP, and net percentage.

Answer 1

The Correct Option is A

- Step 1: Calculate CP of first item. Selling price (SP) = Rs. 1000, profit = 25. Cost price (CP):
\[ \text{CP}_1 = \frac{1000}{1 + \frac{25}{100}} = \frac{1000}{1.25} = \frac{1000 \cdot 4}{5} = 800. \] - Step 2: Calculate CP of second item. SP = Rs. 1000, loss = 20. CP:
\[ \text{CP}_2 = \frac{1000}{1 - \frac{20}{100}} = \frac{1000}{0.8} = \frac{1000 \cdot 5}{4} = 1250. \] - Step 3: Compute total CP and SP. Total CP = $800 + 1250 = 2050$. Total SP = $1000 + 1000 = 2000$.
- Step 4: Determine loss. CP> SP, so loss = $2050 - 2000 = 50$.
- Step 5: Calculate loss percentage. Loss = $\frac{50}{2050} \times 100 \approx 2.439 \approx 2.5$.
- Step 6: Alternative approach. For unequal percentages, compute total CP and SP directly. Verify: $800 \cdot 1.25 = 1000$, $1250 \cdot 0.8 = 1000$. Loss confirms.
- Step 7: Check options. 2.5 loss matches option (1).
- Step 8: Conclusion. The overall loss is 2.5, so option (1) is correct.