A dishonest shopkeeper professes to sell cloth at the cost price but he uses faulty metre rod. His metre rod measures 95cm only. Find his gain per cent.

Options

A. `6.25`
B. `5.26`
C. 5
D. 6

Answer

To solve the problem of the dishonest shopkeeper, we will follow these steps:

### Step 1: Understand the Problem
The shopkeeper claims to sell cloth at the cost price, but he uses a faulty meter rod that measures only 95 cm instead of the full 100 cm. We need to find out his gain percentage.

### Step 2: Define the Cost Price (CP) and Selling Price (SP)
Let's assume the cost price (CP) of 1 meter (100 cm) of cloth is ₹100. Therefore, the cost price for 95 cm of cloth will be:
\[ \text{CP for 95 cm} = \frac{95}{100} \times 100 = ₹95 \]

### Step 3: Determine the Selling Price (SP)
Since the shopkeeper sells 100 cm (1 meter) of cloth at the cost price, the selling price (SP) for 100 cm is:
\[ \text{SP for 100 cm} = ₹100 \]

### Step 4: Calculate the Gain
Now, we can calculate the gain made by the shopkeeper:
\[ \text{Gain} = \text{SP} - \text{CP for 95 cm} \]
\[ \text{Gain} = 100 - 95 = ₹5 \]

### Step 5: Calculate the Gain Percentage
To find the gain percentage, we use the formula:
\[ \text{Gain Percentage} = \left( \frac{\text{Gain}}{\text{CP for 95 cm}} \right) \times 100 \]
Substituting the values:
\[ \text{Gain Percentage} = \left( \frac{5}{95} \right) \times 100 \]
\[ \text{Gain Percentage} = \frac{500}{95} \approx 5.26\% \]

### Final Answer
The gain percentage of the dishonest shopkeeper is approximately **5.26%**.

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