Step 1: Understanding the Question:
A shopkeeper incurs costs from buying and transporting goods, sets a marked price, offers a discount on it, and makes a final sale. We need to calculate his overall percentage profit on the transaction.
Step 2: Key Formula or Approach:
Calculate total Cost Price (CP) including overheads, determine the net CP per unit, calculate the Selling Price (SP) after the discount, and use the profit percentage formula: $\text{Profit %} = \left( \frac{SP - CP}{CP} \right) \times 100$.
Step 3: Detailed Explanation:
First, calculate the total Cost Price (CP) for all 150 calculators.
Purchase cost = 150 calculators $\times$ Rs. 250/calculator = Rs. 37,500.
Additional overhead expenses (transportation and packing) = Rs. 2,500.
Total CP for 150 calculators = $37,500 + 2,500 = 40,000$ Rs.
We can find the CP per calculator to make calculations simpler:
CP per calculator = $\frac{40000}{150} = \frac{800}{3} \approx 266.67$ Rs.
Now, let's determine the final Selling Price (SP) per calculator.
The Marked Price (MP) per calculator is given as Rs. 320.
The shopkeeper gives a 5% discount on this marked price.
Discount amount = 5% of 320 = $0.05 \times 320 = 16$ Rs.
SP per calculator = MP - Discount = $320 - 16 = 304$ Rs.
Next, we calculate the profit earned per calculator.
Profit = SP - CP = $304 - \frac{800}{3}$.
To subtract, find a common denominator: $\frac{912}{3} - \frac{800}{3} = \frac{112}{3}$ Rs.
Finally, calculate the percentage profit based on the cost price.
Percentage Profit = $\left( \frac{\text{Profit}}{\text{CP}} \right) \times 100$
Percentage Profit = $\frac{\frac{112}{3}}{\frac{800}{3}} \times 100$
The denominators of 3 cancel out: $\left( \frac{112}{800} \right) \times 100 = \frac{112}{8}$.
$112 \div 8 = 14$.
The profit percentage gained by the shopkeeper is 14%.
Step 4: Final Answer:
The percentage profit gained by the shopkeeper is 14%.