A shopkeeper marks the price of three identical articles, first, 60% above the Cost Price; second, 45% above the Cost Price and the third, 40% above the cost price. If he gives discount of 25% on first article, 20% on the second article and 15% on the third one, what is his overall profit percentage?
$16\frac{2}{3}$%
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
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Assume the Cost Price (CP) for each of the three identical articles is $100.
The Total Cost Price (CPtotal) is calculated as:
$ CP_{total} = 3 \times \$100 = \$300 $
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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 $
- Marked Price (MP1): Marked 60% above CP.
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Calculate the Total Selling Price (SPtotal) for all three articles:
$ SP_{total} = SP1 + SP2 + SP3 = \$120 + \$116 + \$119 = \$355 $
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Calculate the Total Profit made by the shopkeeper:
$ \text{Total Profit} = SP_{total} - CP_{total} = \$355 - \$300 = \$55 $
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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 $18\frac{1}{3}$%.
Important Questions from Successive Selling
By selling a watch at Rs. 840 a person loses 4%. Find the gain or loss if he sold it for Rs. 875?
Gaurav bought some articles at 5 for Rs. 6 and sold them at 10 for Rs. 11. His loss percentage is:
The increase in the price of a certain item was 25%. Then the price was decreased by 20% and then again increased by 10%. What is the resultant increase in the price?
- The selling price of 24 articles is equal to the cost price of 26 articles. If, due to a change in market conditions, the selling price of each article decreases by $10\%$ and the cost price of each article increases by $5\%$, what will be the new gain or loss percentage (correct to two decimal places)?
X sells goods to Y at a profit of 20 percent and Y sells the same goods to Z at a profit of 50 percent. If the cost price for Z is Rs 9000, then what is the cost of the goods for X?
