Sunaina sold an article to Samir at a profit of 10% , Samir sold  that article to sujal at a profit  of 12%, sujal sold that article to Sanjana at a loss of 20%. Sanjana again sold that article to sunaina at a profit of 5%. Find the overall percentage profit or loss for sunaina

Let's break down the problem step by step to find the overall percentage profit or loss for Sunaina.

### Step 1: Understand the transactions
1. **Sunaina** sold the article to **Samir** at a 10% profit.
2. **Samir** sold the article to **Sujal** at a 12% profit.
3. **Sujal** sold the article to **Sanjana** at a 20% loss.
4. **Sanjana** sold the article back to **Sunaina** at a 5% profit.

### Step 2: Let the cost price for Sunaina be \( C \)
- When Sunaina sells to Samir at a 10% profit, the selling price (SP) for Samir is:
  \[
  SP_{\text{Samir}} = C \times \left(1 + \frac{10}{100}\right) = 1.1C
  \]

- When Samir sells to Sujal at a 12% profit, the selling price (SP) for Sujal is:
  \[
  SP_{\text{Sujal}} = 1.1C \times \left(1 + \frac{12}{100}\right) = 1.1C \times 1.12 = 1.232C
  \]

- When Sujal sells to Sanjana at a 20% loss, the selling price (SP) for Sanjana is:
  \[
  SP_{\text{Sanjana}} = 1.232C \times \left(1 - \frac{20}{100}\right) = 1.232C \times 0.8 = 0.9856C
  \]

- When Sanjana sells back to Sunaina at a 5% profit, the selling price (SP) for Sunaina is:
  \[
  SP_{\text{Sunaina}} = 0.9856C \times \left(1 + \frac{5}{100}\right) = 0.9856C \times 1.05 = 1.03488C
  \]

### Step 3: Calculate the overall percentage profit or loss for Sunaina
- The final cost for Sunaina is \( 1.03488C \).
- The initial cost for Sunaina was \( C \).

The overall profit percentage can be calculated as:
\[
\text{Overall Profit Percentage} = \left(\frac{1.03488C - C}{C}\right) \times 100 = (1.03488 - 1) \times 100 = 0.03488 \times 100 = 3.488\%
\]

### Conclusion:
The overall percentage profit for Sunaina is **3.488%**.

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Would you like more details on any of these steps, or do you have any questions?

Here are some related questions:
1. What if Sunaina sold the article to Samir at a 20% profit instead?
2. How would the result change if Sujal had made a 10% profit instead of a loss?
3. What would be the overall loss if Sanjana sold the article back to Sunaina at a 10% loss?
4. How does the final selling price change if each party makes a 10% profit instead of varying profits?
5. Can you calculate the profit or loss for each individual involved?

**Tip:** To calculate profit or loss percentages effectively, always work step by step and keep track of each transaction's impact on the original cost.

Learn how to calculate the overall percentage profit or loss for Sunaina through a series of transactions involving profit and loss percentages. This detailed solution breaks down each step, including cost price calculations and final profit percentage determination. Suitable for high school students learning about profit and loss calculations.

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