A shopkeeper professes to sell his goods on cost price but uses 750gms instead of 1 kg. What is his gain in percentage?

The correct option is 33.33.

Step-by-step Explanation:

Let us assume that the cost price (CP) of 1 gram of goods is 1 unit.
Since 1 kg is equal to 1000 grams, the cost price of 1 kg is:
CP of 1000 g = 1000 units

The shopkeeper claims to sell his goods at cost price, meaning he charges the customer the cost price of a full 1 kg (1000 grams).
Therefore, the Selling Price (SP) of the goods sold is:
SP = 1000 units

However, the shopkeeper actually uses a weight of 750 grams instead of 1 kg.
The actual cost price (CP) of the 750 grams of goods he provides is:
CP of 750 g = 750 units

Now, we calculate the shopkeeper's gain using the formula:
Gain = Selling Price - Cost Price

Substituting the values:
$$\mathrm{Gain}=1000-750=250\text{units}$$

The gain percentage is calculated relative to the cost of the goods actually sold (750 grams):
$$\text{Gain Percentage}=\left(\frac{\mathrm{Gain}}{\text{Cost Price of goods sold}}\right)\times 100$$

Substituting the gain and cost price values:
$$\text{Gain Percentage}=\left(\frac{250}{750}\right)\times 100$$

Simplifying the fraction:
$$\text{Gain Percentage}=\frac{1}{3}\times 100$$

Calculating the percentage:
$$\text{Gain Percentage}\approx 33.33\%$$

Thus, the shopkeeper's gain is 33.33%.