An item costing Rs. 840 was sold by a shopkeeper at a gain of 10% and it was again sold by the new buyer at a loss of 5%. Final selling price of the item is :

Options

A. Rs. 877.80
B. Rs. 798
C. Rs. 924
D. Rs. 37.80

Answer

To solve the problem step by step, we will calculate the selling price of the item after the shopkeeper's gain and the new buyer's loss.

### Step 1: Calculate the Selling Price after the Shopkeeper's Gain
1. **Cost Price (CP)** of the item = Rs. 840
2. **Gain Percentage** = 10%
3. **Gain Amount** = (Gain Percentage / 100) × CP
\[ \text{Gain Amount} = \frac{10}{100} \times 840 = 84 \]
4. **Selling Price (SP) after gain** = CP + Gain Amount
\[ \text{SP} = 840 + 84 = 924 \]

### Step 2: Calculate the Selling Price after the New Buyer's Loss
1. **New Cost Price (CP)** for the new buyer = Rs. 924 (the selling price from the shopkeeper)
2. **Loss Percentage** = 5%
3. **Loss Amount** = (Loss Percentage / 100) × New CP
\[ \text{Loss Amount} = \frac{5}{100} \times 924 = 46.2 \]
4. **Final Selling Price (SP) after loss** = New CP - Loss Amount
\[ \text{Final SP} = 924 - 46.2 = 877.8 \]

### Final Answer
The final selling price of the item is **Rs. 877.80**.

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