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

Concept: In dishonest weighing problems, the seller charges for one quantity but delivers a smaller quantity. Actual profit must be calculated using the real quantity supplied and the amount received.

Step 1: Assume the cost price of 1 kg is ₹100.
Then, \[ CP=₹100. \] He claims a loss of \(10\%\). Thus selling price charged for \(1\) kg is \[ SP=100-10=₹90. \]

Step 2: Determine the actual cost of goods delivered.
He delivers only \(800\) g. Cost of \(800\) g \[ = 100\times\frac{800}{1000} = ₹80. \]

Step 3: Calculate actual profit.
Amount received \[ =₹90. \] Actual cost \[ =₹80. \] Profit \[ =90-80 = ₹10. \]

Step 4: Find profit percentage.
\[ \text{Profit \%} = \frac{10}{80}\times100 = 12.5\%. \] Hence, \[ \boxed{12.5\%\text{ profit}} \]