Question

A dishonest shop owner advertises to sell his goods at Cost Price. But he uses a weight of 900 gms for a kg of weight. What is his gain %?

• A. 11 1/9 %
• B. 11 1/8 %
• C. 11 1/7 %
• D. 11 1/5 %

Hint:

For false weight problems where goods are sold at cost price, the gain is always calculated on the quantity the shopkeeper actually parts with (the false weight), not the quantity he claims to sell. The profit comes from the goods he saved.

Answer 1

The Correct Option is A

Step 1: Understanding the Problem
This is a classic "false weight" problem. The shopkeeper claims to sell at the cost price (CP), which means his profit comes from cheating on the weight. He charges the customer for 1 kg (1000 gms) but only gives them 900 gms.

Step 2: Key Formula or Approach
In false weight problems, the gain percentage is calculated on the actual amount of goods sold (the true weight used). Let's assume the cost price of 1 gm of goods is 1 rupee.

The shopkeeper's Cost Price (CP) = Cost of the goods he actually gives = Cost of 900 gms = 900 rupees.
The shopkeeper's Selling Price (SP) = Price he charges the customer = Price of 1000 gms = 1000 rupees.
The gain percentage formula is: \[ \text{Gain %} = \frac{\text{SP} - \text{CP}}{\text{CP}} \times 100% \] A shortcut formula for this specific case is: \[ \text{Gain %} = \frac{\text{Error}}{\text{True Value} - \text{Error}} \times 100% = \frac{\text{Error}}{\text{False Weight}} \times 100% \]
Step 3: Detailed Explanation
Method 1: Using CP and SP
CP = 900 (cost of what he gives)
SP = 1000 (what he charges for)
Gain = SP - CP = 1000 - 900 = 100
\[ \text{Gain %} = \frac{\text{Gain}}{\text{CP}} \times 100% = \frac{100}{900} \times 100% = \frac{1}{9} \times 100% = 11.11...% \] To convert this to a mixed fraction, we divide 100 by 9. 100 \(\div\) 9 = 11 with a remainder of 1. So, the percentage is \( 11 \frac{1}{9}% \).
Method 2: Using the Shortcut Formula
True Value = 1000 gms
False Weight = 900 gms
Error = True Value - False Weight = 1000 - 900 = 100 gms
\[ \text{Gain %} = \frac{\text{Error}}{\text{False Weight}} \times 100% = \frac{100}{900} \times 100% = \frac{1}{9} \times 100% = 11 \frac{1}{9}% \]
Step 4: Final Answer
The shop owner's gain is \( 11 \frac{1}{9}% \). Therefore, option (A) is the correct answer.