Sumit purchased an item for र 4000 and sold it at the gain of 35%. From that amount, he purchased another item and sold it at the loss of 20%. What is his over all gain/loss?

Options

A. Loss of र 340
B. Gain of र 320
C. Loss of र 360
D. Neither gain nor loss

Answer

To solve the problem step by step, we will follow the calculations as described in the video transcript.

### Step 1: Calculate the Selling Price (SP1) after the first purchase.
- **Given:**
- Cost Price (CP1) = ₹4000
- Gain = 35%

- **Formula for Selling Price (SP):**
\[ SP = CP \times \left(1 + \frac{\text{Gain \%}}{100}\right) \]

- **Calculation:**
\[ SP1 = 4000 \times \left(1 + \frac{35}{100}\right) = 4000 \times \frac{135}{100} = 4000 \times 1.35 = 5400 \]

### Step 2: Calculate the Cost Price (CP2) for the second item.
- **From Step 1, we have:**
- CP2 = SP1 = ₹5400

### Step 3: Calculate the Selling Price (SP2) after the second purchase.
- **Given:**
- Loss = 20%

- **Formula for Selling Price (SP) when there is a loss:**
\[ SP = CP \times \left(1 - \frac{\text{Loss \%}}{100}\right) \]

- **Calculation:**
\[ SP2 = 5400 \times \left(1 - \frac{20}{100}\right) = 5400 \times \frac{80}{100} = 5400 \times 0.8 = 4320 \]

### Step 4: Calculate the overall gain or loss.
- **Initial Investment (CP1) = ₹4000**
- **Final Selling Price (SP2) = ₹4320**

- **Calculation of Gain:**
\[ \text{Gain} = SP2 - CP1 = 4320 - 4000 = 320 \]

### Conclusion:
Sumit has an overall gain of ₹320.

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