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: $\frac{11}{10} x - \frac{11}{100} x = (\frac{110 - 11}{100}) x = \frac{99}{100} x$ .
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: $\frac{Gain}{Original Cost} \times 100 = \frac{\frac{x}{100}}{x} \times 100 = 1 %$ .
Therefore, Gopal experiences a gain of 1%.

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.