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
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