Question

A dishonest trader claims to sell at a loss of 16%. However, he uses a false scale and in realty makes a profit of 20%. To what difference does he defraud his customers when he claims to sell 1 kg of an item?

• A. 30 gms
• B. 100 gms
• C. 200 gms
• D. 300 gms

Answer 1

The Correct Option is D

Finding the Fraud Quantity in the Trader's Claim

Step 1: Understand the Trader's Claim 

• The trader claims to sell at a 16% loss, meaning if the cost price is Rs. 100, the claimed selling price is:
• However, he actually makes a 20% profit, meaning the real selling price is:
• The trader uses a false scale while selling 1 kg of an item.

Step 2: Find the Actual Weight Given

The price per kg of the item is assumed to be Rs. 84 as per his claim.

Since the trader actually receives Rs. 120 but charges based on Rs. 84 per kg, the actual weight given can be calculated as:

\[ \text{Actual Weight Given} = \frac{\text{Claimed Selling Price}}{\text{Actual Selling Price per kg}} \]

Substituting values:

\[ \frac{84}{120} \times 1 \text{ kg} = 0.7 \text{ kg} = 700 \text{ grams} \]

Step 3: Find the Fraud Quantity

The trader claims to sell 1 kg but actually gives only 700 grams. The amount he defrauds is:

\[ 1000 - 700 = 300 \text{ grams} \]

Final Answer:

Thus, the correct answer is (D) 300 grams.