Seema bought a mobile and laptop at a certain price. She sold the mobile at 10% gain and laptop at 25% gain. She found that the cost price of the mobile is equal to the selling price of the laptop. Find her profit percentage.
16 \(\frac{2}{3}\)%
Let the cost price of the mobile be \( M \) and the cost price of the laptop be \( L \).
The mobile is sold at a 10% gain, so the selling price of mobile is:
\[ \text{Selling Price of Mobile} = M + \frac{10}{100}M = 1.1M \]
The laptop is sold at a 25% gain, so the selling price of the laptop is:
\[ \text{Selling Price of Laptop} = L + \frac{25}{100}L = 1.25L \]
According to the problem, the cost price of the mobile is equal to the selling price of the laptop:
\[ M = 1.25L \]
Now, we need to find the total cost price and the total selling price:
The total cost price is:
\[ \text{Total Cost Price} = M + L \]
The total selling price is:
\[ \text{Total Selling Price} = 1.1M + 1.25L \]
Substitute \( M = 1.25L \) into the total selling price:
\[ \text{Total Selling Price} = 1.1(1.25L) + 1.25L \]
\[ = 1.375L + 1.25L \]
\[ = 2.625L \]
The total cost price using \( M = 1.25L \) is:
\[ \text{Total Cost Price} = 1.25L + L = 2.25L \]
Total profit is the difference between total selling price and total cost price:
\[ \text{Profit} = 2.625L - 2.25L = 0.375L \]
The profit percentage is calculated as:
\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{\text{Total Cost Price}}\right) \times 100 \]
\[ = \left(\frac{0.375L}{2.25L}\right) \times 100 \]
\[ = \left(\frac{0.375}{2.25}\right) \times 100 \]
\[ = \frac{1}{6} \times 100 \]
\[ = 16.67\%\]
Therefore, Seema's profit percentage is 16 \(\frac{2}{3}\)%.
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?
