Calculating Gain Percentage on Pen Sales
The problem asks us to find the gain percentage when a shopkeeper's gain is equivalent to the selling price (SP) of 40 pens, achieved after selling 200 pens.
Understanding the Gain
The shopkeeper sold 200 pens. The profit (Gain) made is equal to the selling price of 40 pens.
- Let the Selling Price (SP) of one pen be $S$.
- Let the Cost Price (CP) of one pen be $C$.
Total SP for 200 pens = $200 \times S$.
Total Gain = SP of 40 pens = $40 \times S$.
We know that Gain = Total SP - Total CP.
Therefore, the Total CP for the 200 pens must be the SP of the remaining pens:
Total CP for 200 pens = Total SP for 200 pens - Gain
Total CP for 200 pens = $(200 \times S) - (40 \times S) = 160 \times S$.
This means the cost price of 200 pens is equal to the selling price of 160 pens.
Gain Percentage Calculation
The formula for Gain Percentage is:
Gain Percentage = $\frac{Gain}{Total CP} \times 100\%$
Substitute the values we found:
Gain Percentage = $\frac{40 \times S}{160 \times S} \times 100\%$
Cancel out $S$:
Gain Percentage = $\frac{40}{160} \times 100\%$
Simplify the fraction:
Gain Percentage = $\frac{1}{4} \times 100\%$
Gain Percentage = $25\%$
The gain percentage is $25\%$.
Similar Questions
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Important Questions from Profit and Loss
By selling an article for Rs. 2,200, a profit of 10% is earned. If the same article is sold for Rs. 2,600, then what will be the gain percentage?
By selling an article for Rs. 640, a person loses 15% of its selling price. At what price (in Rs.) should he sell it to gain 15% on its cost price?
The selling prices of articles A and B are the same. A is sold at a profit of 28 percent and B is sold at a loss of 24 percent. If the total selling price of the both articles is Rs. 48640, then what is the cost price of A and B, respectively ?
The cost price of an article is Rs. 2800. Profit as a percentage of selling price is 20 percent. What is the actual profit (in Rs.) ?
A trader bought 640 kg of rice. He sold a part of rice at 20% profit and the rest at 5% loss. He earned a profit of 15% in the entire transaction. What is the quantity (in kg) of rice that he sold at 5% loss?
