By selling an umbrella for Rs. 30, a shopkeeper gains 20%. During a clearance sale, the shopkeeper allows a discount of 10%. Find his gain percent during the sale season.

Options

A. 8
B. 7
C. 9
D. 7 `1/2`

Answer

To solve the problem step by step, we will follow the given information and perform the necessary calculations.

### Step 1: Determine the Cost Price (CP)
The selling price (SP) of the umbrella is given as Rs. 30, and the gain is 20%.

To find the cost price (CP), we can use the formula:
\[ SP = CP + \text{Gain} \]
Since Gain is 20% of CP, we can express it as:
\[ SP = CP + 0.2 \times CP = 1.2 \times CP \]
Now, substituting the selling price:
\[ 30 = 1.2 \times CP \]
To find CP, we rearrange the equation:
\[ CP = \frac{30}{1.2} = 25 \]

### Step 2: Calculate the Discount
During the clearance sale, a discount of 10% is given on the selling price of Rs. 30.

The amount of discount can be calculated as:
\[ \text{Discount} = 10\% \text{ of } 30 = \frac{10}{100} \times 30 = 3 \]

### Step 3: Determine the New Selling Price (SP)
Now, we can find the new selling price after applying the discount:
\[ \text{New SP} = \text{Original SP} - \text{Discount} = 30 - 3 = 27 \]

### Step 4: Calculate the Gain During the Sale
Now, we need to find the gain during the sale. The gain can be calculated as:
\[ \text{Gain} = \text{New SP} - CP = 27 - 25 = 2 \]

### Step 5: Calculate the Gain Percentage
Finally, we can find the gain percentage using the formula:
\[ \text{Gain Percentage} = \left( \frac{\text{Gain}}{CP} \right) \times 100 \]
Substituting the values:
\[ \text{Gain Percentage} = \left( \frac{2}{25} \right) \times 100 = 8\% \]

### Final Answer
The gain percentage during the sale season is **8%**.

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