Calculating Dishonest Shopkeeper's Gain Percent

This problem involves a dishonest shopkeeper who employs two methods to increase profit: selling at a higher price than the cost price and short-weighing the product.

Understanding the Dishonesty

The shopkeeper:

• Buys sugar at Rs. 40 per kg (Cost Price).
• Sells sugar at Rs. 45 per kg (Stated Selling Price).
• Gives only 900 gm for every 1 kg packet.

To calculate the actual gain percent, we need to determine the effective cost price of the quantity he actually sells and the effective selling price he charges for that quantity.

Calculating Effective Cost Price (CP)

The shopkeeper pays the cost price for the sugar he buys. For a nominal 1 kg (1000 gm), his cost is Rs. 40. However, he only gives 900 gm to the customer.

So, we need to find the cost price of the 900 gm quantity that the customer actually receives.

Cost of 1000 gm = Rs. 40

Cost of 1 gm = \(\frac{40}{1000}\) Rs.

Effective Cost Price of 900 gm = Cost of 1 gm \(\times\) 900

\(\text{Effective CP} = \frac{40}{1000} \times 900 = \frac{40 \times 9}{10} = 4 \times 9 = 36\) Rs.

So, the actual cost incurred by the shopkeeper for the quantity he sells (900 gm) is Rs. 36.

Calculating Effective Selling Price (SP)

The shopkeeper charges the customer for 1 kg, even though he only gives 900 gm. The selling price for 1 kg is stated as Rs. 45.

Effective Selling Price for the 900 gm sold = Price of 1 kg

\(\text{Effective SP} = 45\) Rs.

So, the shopkeeper sells the 900 gm quantity for Rs. 45.

Calculating Gain

Gain is the difference between the Effective Selling Price and the Effective Cost Price for the quantity sold.

\(\text{Gain} = \text{Effective SP} - \text{Effective CP}\)

\(\text{Gain} = 45 - 36 = 9\) Rs.

The shopkeeper makes a gain of Rs. 9 on the quantity he sells.

Calculating Gain Percent

Gain percent is calculated on the Effective Cost Price.

\(\text{Gain Percent} = \frac{\text{Gain}}{\text{Effective CP}} \times 100\%\)

\(\text{Gain Percent} = \frac{9}{36} \times 100\%\)

\(\text{Gain Percent} = \frac{1}{4} \times 100\%\)

\(\text{Gain Percent} = 25\%\)

The gain percent of the dishonest shopkeeper is 25%.

Revision Table: Key Concepts in Profit and Loss with Dishonesty

Additional Information: Types of Dishonesty in Business

Shopkeepers or sellers can employ various deceptive practices to increase their profit margins. Understanding these helps in solving related problems:

• Short-weighing: Using false weights or scales to give less quantity than paid for. This is the method used in the problem (100 gm less per kg).
• Adulteration: Mixing cheaper substances with the product (e.g., mixing water in milk, stones in grains) to increase volume or weight at a lower cost.
• Selling at higher price: Simply marking up the selling price significantly compared to the cost price, sometimes disguised as a discount on a fake higher price.
• Using false measures: Similar to short-weighing but with volume or length measurements.
• Selling inferior quality: Charging the price of high-quality goods while selling lower-quality ones.

Problems involving dishonest shopkeepers often combine price manipulation with quantity manipulation (like short-weighing), requiring careful calculation of the actual cost and selling price for the real quantity exchanged.