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We are given the following problem:

- The cost price (C.P.) of 10 apples is equal to the selling price (S.P.) of 7 bananas.
- We are asked to find the profit percentage when 1 apple is sold for the selling price of 4 bananas.

### Let’s break down the solution:

1. **Let the cost price of 1 apple be** \( C \) (the cost price of 10 apples is \( 10C \)).

2. **Let the selling price of 1 banana be** \( S_b \) (the selling price of 7 bananas is \( 7S_b \)).

We are given that the cost price of 10 apples is equal to the selling price of 7 bananas:

\[
10C = 7S_b
\]

This can be rewritten as:

\[
C = \frac{7S_b}{10}
\]

3. Now, the selling price of 1 apple is equal to the selling price of 4 bananas. So, the selling price of 1 apple \( S_a \) is:

\[
S_a = 4S_b
\]

4. **Profit** is the difference between the selling price and the cost price:

\[
\text{Profit} = S_a - C = 4S_b - \frac{7S_b}{10}
\]

Let’s simplify the profit expression:

\[
\text{Profit} = \frac{40S_b}{10} - \frac{7S_b}{10} = \frac{33S_b}{10}
\]

5. **Profit percentage** is calculated as:

\[
\text{Profit percentage} = \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100 = \left( \frac{\frac{33S_b}{10}}{\frac{7S_b}{10}} \right) \times 100 = \frac{33}{7} \times 100
\]

\[
\text{Profit percentage} = 471.43\%
\]

### Final Answer:
The profit percentage is **471.43%**.

Would you like further clarification on any steps?

Here are five related questions to explore this further:
1. How does the profit percentage change if the cost price is increased?
2. What would be the selling price of 1 apple if there were no profit?
3. How would the profit percentage change if 1 apple were sold for the selling price of 5 bananas?
4. How can you calculate the break-even point between cost price and selling price?
5. How would the profit percentage change if the cost price of 10 apples equals the selling price of 8 bananas?

**Tip:** In profit problems, clearly distinguishing between cost price and selling price is crucial for determining profit percentage accurately.

The cost price of 10 apples is equal to the selling price of 7 bananas. What is the profit percentage in selling 1 apple if 1 apple is sold for the selling price of 4 bananas?

Learn how to calculate the profit percentage when the cost price of 10 apples equals the selling price of 7 bananas, and 1 apple is sold for the selling price of 4 bananas. This problem involves understanding profit calculations and algebraic equations, suitable for Grades 9-12.

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