A fruit seller spends equal sums of money to purchase 2730 pieces of mangoes and 1456 pieces of oranges. The mangoes are sold in such a way that 210 mangoes can be purchased with the sale money of 161 mangoes. With the sale money of 299 oranges ,208 oranges can be bought. Which of the following statement is valid regarding the overall percentage of profit or

Pick ONE option
>10%
<5%
<10% but greater than 5%
No profit no loss

Let's break down the problem step by step to find out which statement is valid regarding the overall percentage of profit or loss.

### Given:
- The seller spends an equal amount of money to purchase **2730 mangoes** and **1456 oranges**.
- **For mangoes:**
  - The sale price of **161 mangoes** is enough to buy **210 mangoes**.
- **For oranges:**
  - The sale price of **299 oranges** is enough to buy **208 oranges**.

We will calculate the profit percentage for both mangoes and oranges separately and then find the overall profit percentage.

### 1. Profit on Mangoes:
Let the **cost price of 1 mango** be \( C_m \).

- The total cost of 2730 mangoes is \( 2730 \times C_m \).
- For 161 mangoes, the sale price is equivalent to buying 210 mangoes, which means the selling price of 1 mango is higher than its cost price.

The ratio of sale price to cost price for mangoes is:
\[
\text{Selling price of 1 mango} = \frac{210}{161} \times C_m
\]
Thus, the profit per mango is:
\[
\text{Profit per mango} = \frac{210}{161} C_m - C_m = C_m \left( \frac{210}{161} - 1 \right)
\]
\[
\text{Profit per mango} = C_m \left( \frac{210 - 161}{161} \right) = C_m \times \frac{49}{161}
\]
The percentage profit on mangoes is:
\[
\text{Profit percentage on mangoes} = \frac{49}{161} \times 100 \approx 30.43\%
\]

### 2. Profit on Oranges:
Let the **cost price of 1 orange** be \( C_o \).

- The total cost of 1456 oranges is \( 1456 \times C_o \).
- For 299 oranges, the sale price is equivalent to buying 208 oranges, which means the selling price of 1 orange is lower than its cost price.

The ratio of sale price to cost price for oranges is:
\[
\text{Selling price of 1 orange} = \frac{208}{299} \times C_o
\]
Thus, the loss per orange is:
\[
\text{Loss per orange} = C_o - \frac{208}{299} C_o = C_o \left( 1 - \frac{208}{299} \right)
\]
\[
\text{Loss per orange} = C_o \times \frac{91}{299}
\]
The percentage loss on oranges is:
\[
\text{Loss percentage on oranges} = \frac{91}{299} \times 100 \approx 30.43\%
\]

### 3. Overall Profit or Loss:
The seller spends an equal amount of money on mangoes and oranges. The profit on mangoes is about 30.43%, while the loss on oranges is about 30.43%. Since the gains and losses cancel each other out, the seller makes:

\[
\text{Overall profit or loss} = 0\%
\]

### Conclusion:
The valid statement is **"No profit no loss."**

Would you like further clarification, or do you have any questions?

Here are 5 related questions:
1. How do you calculate profit percentage for different items?
2. What is the formula for calculating overall profit or loss when handling multiple products?
3. How does the relationship between cost price and selling price affect profit or loss?
4. What would happen if the cost of the oranges was not equal to the cost of the mangoes?
5. How would you calculate profit if the number of mangoes and oranges sold were different?

**Tip:** When dealing with multiple products, it's crucial to handle each product's profit or loss separately before combining them for the overall result.

A fruit seller spends equal sums of money to purchase 2730 pieces of mangoes and 1456 pieces of oranges. The mangoes are sold in such a way that 210 mangoes can be purchased with the sale money of 161 mangoes. With the sale money of 299 oranges, 208 oranges can be bought. Which of the following statement is valid regarding the overall percentage of profit or loss?

Explore how to calculate the overall profit or loss for a fruit seller who spends equal amounts on mangoes and oranges. This detailed explanation uses ratios and percentage calculations to determine the outcome, suitable for students in Grades 9-10.

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