Gopal bought a cell phone and sold it to Ram at 10% profit. Then Ram wanted to sell it back to Gopal at 10% loss. What will be Gopal's position if he agreed?

Correct Option (3)

Let the initial cost price of the cell phone for Gopal be Rs. x.

• Gopal sells the phone to Ram at a 10% profit.
• The selling price for Gopal (which is the cost price for Ram) is calculated as: $x+\frac{10}{100}x=\frac{11}{10}x$.
• Ram then sells the phone back to Gopal at a 10% loss on Ram's purchase price.
• The selling price for Ram (which is the new cost price for Gopal) is calculated as: $\frac{11}{10}x-\frac{10}{100}\times \frac{11}{10}x$.
• Simplifying this expression: $\frac{11}{10}x-\frac{11}{100}x=\left(\frac{110-11}{100}\right)x=\frac{99}{100}x$.
• Gopal's initial outlay for the phone was Rs. x, and he now reacquires it for Rs. $\frac{99}{100}x$.
• Gopal's net financial position is determined by the difference between his initial cost and the price he paid to buy it back: $x-\frac{99}{100}x=\frac{x}{100}$. This represents a gain for Gopal.
• The percentage gain for Gopal is calculated as: $\frac{\text{Gain}}{\text{Original Cost}}\times 100=\frac{\frac{x}{100}}{x}\times 100=1\mathrm{\%}$.
• Therefore, Gopal experiences a gain of 1%.

Incorrect Options:

• Option 1 (Neither loss nor gain): This is incorrect because the sequential transactions result in a quantifiable net financial gain for Gopal.
• Option 2 (Loss 1%): This is incorrect as the detailed calculation demonstrates a profit of 1% for Gopal, not a loss.
• Option 4 (Gain 0.5%): This is incorrect because the precise calculation establishes a gain of 1%, not 0.5%. The percentage change is not a simple average of the profit and loss percentages.