Question

A dishonest dealer claims to sell his goods at a loss of \(10\%\) on cost price but uses a false weight of \(800\) g instead of \(1\) kg. Find his actual profit or loss percentage.

• A. \(12.5\%\) profit
• B. \(10\%\) loss
• C. \(11.11\%\) profit
• D. \(25\%\) profit

Hint:

In false-weight questions, first find the actual quantity delivered. Then calculate profit using the real cost of that quantity.

Answer 1

The Correct Option is A

Step 1: Understand the trick.
The dealer says he sells at a loss, but he cheats on the weight. He gives only $800$ g while charging for a full $1$ kg. This hidden saving can turn his claimed loss into a real profit.

Step 2: Assume an easy cost price.
Let the cost of $1$ kg be rupees $100$. This makes the numbers simple to work with. \[ CP\text{ of }1\text{ kg}=\text{Rs }100. \]
Step 3: Find the price he charges.
He claims a loss of $10\%$, so the price he charges for what he calls $1$ kg is \[ 100-10=\text{Rs }90. \] So the buyer pays him rupees $90$.

Step 4: Find the real cost of what he actually gives.
He hands over only $800$ g. The true cost of $800$ g is \[ 100\times\frac{800}{1000}=\text{Rs }80. \]
Step 5: Find the actual profit.
He receives rupees $90$ but the goods cost him only rupees $80$. So his profit is \[ 90-80=\text{Rs }10. \]
Step 6: Convert the profit into a percentage.
Profit percent is found on the actual cost of $80$: \[ \frac{10}{80}\times100=12.5\%. \] So he actually makes a profit of $12.5\%$. \[ \boxed{12.5\%\text{ profit}} \]