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
- I bought two frocks for ₹1,200. I sold the first one at a loss of 7% and the second at a gain of 23%. If, on the whole I made neither a loss nor a gain, find the cost price (in ₹) of the first frock.
- The selling price of 40 books is equal to the cost price of 28 books. Find the loss or gain percentage.
- Big Mart is offering $5\%$ discount on card payment. How much percentage above cost price should the marked price be so as to make a profit of $10\%$?
- If a shopkeeper added $20\%$ on the cost price as marked price and gave $20\%$ discount, then how much was his profit or loss percent?
- What is the cost price of articles sold for ₹390 if $20\%$ is the total gain?
- If the selling price of an article is 3 times the discount offered and if the percentage of the discount is equal to the percentage profit, find the ratio of the discount offered to the cost price.
- A vendor purchases an article for ₹500 and sells it for ₹550. What is the percentage gain?
- Rupert purchases a second-hand TV for ₹4,600, spends some money on its repairs, and then sells it for ₹5,406, thereby earning a profit of 6%. How much did Rupert spend on the repairs?
- Atulit buys an old bicycle for ₹4,000 and spends ₹400 towards its repairs. If he sells the bicycle for ₹5,000, his percentage gain is:
- I bought two pendants for ₹1,200. I sold the first one at a loss of 10% and the second at a gain of 14%. If, on the whole I made neither a loss nor a gain, find the cost price (in ₹) of the first pendant.
Important Questions from Profit and Loss
Rohit buys 8 pens and 4 pencils for Rs. 2400. He sells pencils at a profit of 20 percent and pens at the loss of 10 percent. If his overall profit is Rs. 240, then what is the sum of the cost price of one pen and one pencil?
A man sells a car to his friend at the loss of 10 %; who in return sells it for Rs. 54000 making a profit of 20 %. What was the initial value of the car?
An article was sold at a loss of 24%. If it were sold for Rs. 1,596 more, then there would have been a gain of 18%, The cost price of the article is:
The cost price of an article is Rs.6,450. If it sold at a profit 16%, how much would be its selling price?
If the selling price of 7 articles is equal to the cost price of 6 articles, then what is the percentage loss?
