Sumit purchased an item for Rs 6500 and sold it at the gain of 24%. 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 Rs 42
B. Gain of Rs 42
C. loss of Rs 52
D. Neither gain nor loss

Answer

To solve the problem step by step, we will calculate the selling price (SP) of the first item after a gain of 24%, then use that amount to find the cost price (CP) of the second item. Finally, we will calculate the selling price of the second item after a loss of 20% and determine the overall gain or loss.

### Step 1: Calculate the Selling Price of the First Item
- **Cost Price (CP) of the first item** = Rs 6500
- **Gain Percentage** = 24%

The formula for Selling Price (SP) with gain is:
\[ SP = CP \times \left(1 + \frac{\text{Gain Percentage}}{100}\right) \]

Substituting the values:
\[ SP = 6500 \times \left(1 + \frac{24}{100}\right) = 6500 \times \left(1 + 0.24\right) = 6500 \times 1.24 \]
\[ SP = 6500 \times 1.24 = 8060 \]

### Step 2: Calculate the Cost Price of the Second Item
The selling price of the first item becomes the cost price of the second item:
- **Cost Price (CP) of the second item** = Rs 8060

### Step 3: Calculate the Selling Price of the Second Item
- **Loss Percentage** = 20%

The formula for Selling Price (SP) with loss is:
\[ SP = CP \times \left(1 - \frac{\text{Loss Percentage}}{100}\right) \]

Substituting the values:
\[ SP = 8060 \times \left(1 - \frac{20}{100}\right) = 8060 \times \left(1 - 0.20\right) = 8060 \times 0.80 \]
\[ SP = 8060 \times 0.80 = 6448 \]

### Step 4: Calculate Overall Gain or Loss
Now, we need to compare the initial cost price of the first item with the final selling price of the second item:
- **Initial Cost Price (CP)** = Rs 6500
- **Final Selling Price (SP)** = Rs 6448

To find the overall gain or loss:
\[ \text{Loss} = CP - SP = 6500 - 6448 = 52 \]

### Conclusion
Sumit has an overall loss of Rs 52.

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