Question

Two watches were sold at the same price. One was sold at $10 \%$ profit and the other was sold at $10 \%$ loss. Find the overall profit/loss percentage made in the transaction.

• A. $1 \%$ profit
• B. $1 \%$ loss
• C. $2 \%$ profit
• D. $2 \%$ loss

Answer 1

Answer: (B)

Let the selling price of each watch be $₹ 100$. Let us call the watches, which are sold at profit and at loss by Watch 1 and Watch 2, respectively. Let the cost prices of Watch 1 and Watch 2 be $₹ x$ and $₹ \gamma$, respectively.
$\therefore x+\frac{10}{100} x=100 $
$x=\frac{1000}{11}$
$\gamma-\frac{10}{100} \gamma=100$
$\Rightarrow \gamma=\frac{1000}{9} $
$\text { Total cost price (in } ₹)=x+\gamma=\frac{20,000}{99} $
$\text { Total selling price }=₹ 200 $
$\text { Total cost price }>\text { Total selling price }$
$\text { Overall loss (in } ₹ \text { ) }=\frac{20,000}{99}-200=₹ \frac{200}{99} $
$\therefore \text { Overall loss percentage }=\frac{\frac{200}{99}}{\frac{20,000}{99}}$
$\text { (100)\% } 1 \%$