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…

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: $x + \frac{10}{100}x = \frac{11}{10}x$x+10010​x=1011​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$1011​x−10010​×1011​x.
• Simplifying this expression: $\frac{11}{10}x - \frac{11}{100}x = \left( \frac{110 - 11}{100} \right)x = \frac{99}{100}x$1011​x−10011​x=(100110−11​)x=10099​x.
• Gopal's initial outlay for the phone was Rs. x, and he now reacquires it for Rs. $\frac{99}{100}x$10099​x.
• Gopal's net financial position is determined by the difference between his initial cost and the price he paid to buy it back: $x - \frac{99}{100}x = \frac{x}{100}$x−10099​x=100x​. This represents a gain for Gopal.
• The percentage gain for Gopal is calculated as: $\frac{\text{Gain}}{\text{Original Cost}} \times 100 = \frac{\frac{x}{100}}{x} \times 100 = 1\%$Original CostGain​×100=x100x​​×100=1%.
• 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.