The marked price of a saree is Rs. 200. After allowing a discount of 20% on the marked price, the shopkeeper makes a profit of Rs. 16. Find the gain percent.

Options

A. `11(1)/(9)%`
B. `9(1)/(11)%`
C. `11%`
D. `8%`

Answer

To solve the problem step by step, let's break it down:

### Step 1: Determine the Discount Amount
The marked price (MP) of the saree is Rs. 200. The discount given is 20%.

**Calculation:**
- Discount = 20% of MP
- Discount = 20/100 * 200 = Rs. 40

**Hint:** Remember that the discount is calculated as a percentage of the marked price.

### Step 2: Calculate the Selling Price (SP)
The selling price can be calculated by subtracting the discount from the marked price.

**Calculation:**
- Selling Price (SP) = MP - Discount
- SP = 200 - 40 = Rs. 160

**Hint:** The selling price is what the customer pays after the discount is applied.

### Step 3: Find the Cost Price (CP)
We know that the shopkeeper makes a profit of Rs. 16. To find the cost price, we can rearrange the profit formula.

**Calculation:**
- Profit = SP - CP
- Therefore, CP = SP - Profit
- CP = 160 - 16 = Rs. 144

**Hint:** Profit is the difference between the selling price and the cost price.

### Step 4: Calculate the Gain Percent
Gain percent is calculated using the formula:
\[ \text{Gain Percent} = \left( \frac{\text{Profit}}{\text{CP}} \right) \times 100 \]

**Calculation:**
- Gain Percent = (16 / 144) * 100
- Gain Percent = (1/9) * 100 = 11.11%

**Hint:** To find the gain percent, always divide the profit by the cost price and multiply by 100.

### Final Answer
The gain percent is approximately **11.11%**.