Cost Price vs Selling Price Relationship
Let CP denote the cost price of one pen and SP denote the selling price of one pen.
The problem states that the cost price of 19 pens is equal to the selling price of 16 pens.
This can be written as an equation:
$19 \times \text{CP} = 16 \times \text{SP}$
Deriving Price Ratio
To find the relationship between CP and SP, we rearrange the equation to get the ratio:
$\frac{\text{CP}}{\text{SP}} = \frac{16}{19}$
This ratio tells us that for every 16 units of cost price, the selling price is 19 units.
Calculating Percentage Gain
Gain occurs when the selling price is greater than the cost price.
Gain = SP - CP
Using the ratio values, let CP = 16 units and SP = 19 units.
Gain = $19 - 16 = 3$ units
The formula for percentage gain is:
$\text{Percentage Gain} = \left(\frac{\text{Gain}}{\text{CP}}\right) \times 100\%$
Substitute the values:
$\text{Percentage Gain} = \left(\frac{3}{16}\right) \times 100\%$
Calculate the value:
$\text{Percentage Gain} = \frac{300}{16}\%$
Simplify the fraction:
$\text{Percentage Gain} = \frac{75}{4}\%$
Convert to a mixed number:
$\text{Percentage Gain} = 18\frac{3}{4}\%$
Final Answer
The percentage gain is $18\frac{3}{4}\%$.
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?
