A dishonest vendor claims that he is selling goods at their cost price. But he is weighing 902 grams for 1000 grams. What is his profit percentage (rounded off to 2 decimal places)?

The correct option is 10.86%.

Step-by-step Explanation:

1. Understand the Cost Price and Selling Price relationship:
Let the cost price of 1 gram of goods be ₹1.
The vendor claims to sell goods at their cost price. Therefore, the selling price of 1000 grams of goods is set to ₹1000.

2. Calculate the actual cost to the vendor:
Instead of providing 1000 grams, the vendor actually gives 902 grams of goods to the customer.
Since 1 gram costs ₹1, the cost price of 902 grams to the vendor is:

$\text{Cost Price (CP)}=\text{₹902}$

3. Determine the vendor's profit:
The vendor receives ₹1000 from the customer (Selling Price) but only spends ₹902 worth of goods (Cost Price).

$\text{Profit}=\text{Selling Price (SP)}-\text{Cost Price (CP)}$

$\text{Profit}=1000-902=98$

4. Calculate the Profit Percentage:
The profit percentage is always calculated based on the actual Cost Price (CP) incurred by the seller:

$\text{Profit Percentage}=\left(\frac{\text{Profit}}{\text{Cost Price}}\right)\times 100$

$\text{Profit Percentage}=\left(\frac{98}{902}\right)\times 100$

$\text{Profit Percentage}=\frac{9800}{902}\approx 10.8647\%$

Rounding off to two decimal places gives 10.86%.