Calculating Overall Profit Percentage

This solution determines the shopkeeper's overall profit percentage. It involves calculating the selling price (SP) for each of the three articles based on their cost price (CP), marked price (MP), and the discount given, then finding the total profit.

Step-by-Step Calculation for Profit Percentage

1. Assume the Cost Price (CP) for each of the three identical articles is $100.

   The Total Cost Price (CP_total) is calculated as:

   $ CP_{total} = 3 \times \$100 = \$300 $

2. Calculate the Marked Price (MP) and Selling Price (SP) for each article:

   Article 1 Details

   • Marked Price (MP1): Marked 60% above CP.

     $ MP1 = \$100 \times (1 + 0.60) = \$100 \times 1.60 = \$160 $

   • Selling Price (SP1): Given a 25% discount on MP1.

     $ SP1 = \$160 \times (1 - 0.25) = \$160 \times 0.75 = \$120 $

   Article 2 Details

   • Marked Price (MP2): Marked 45% above CP.

     $ MP2 = \$100 \times (1 + 0.45) = \$100 \times 1.45 = \$145 $

   • Selling Price (SP2): Given a 20% discount on MP2.

     $ SP2 = \$145 \times (1 - 0.20) = \$145 \times 0.80 = \$116 $

   Article 3 Details

   • Marked Price (MP3): Marked 40% above CP.

     $ MP3 = \$100 \times (1 + 0.40) = \$100 \times 1.40 = \$140 $

   • Selling Price (SP3): Given a 15% discount on MP3.

     $ SP3 = \$140 \times (1 - 0.15) = \$140 \times 0.85 = \$119 $

3. Calculate the Total Selling Price (SP_total) for all three articles:

   $ SP_{total} = SP1 + SP2 + SP3 = \$120 + \$116 + \$119 = \$355 $

4. Calculate the Total Profit made by the shopkeeper:

   $ \text{Total Profit} = SP_{total} - CP_{total} = \$355 - \$300 = \$55 $

5. Calculate the Overall Profit Percentage:

   The formula for profit percentage is: Profit % = (Total Profit / Total CP) $\times 100%

   $ \text{Overall Profit %} = \frac{\$55}{\$300} \times 100\% $

   $ \text{Overall Profit %} = \frac{55}{3} \% $

   $ \text{Overall Profit %} = 18\frac{1}{3}\% $

Conclusion on Profit Percentage

Based on the calculations derived directly from the problem statement, the shopkeeper's overall profit percentage is $18\frac{1}{3}$%.