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To solve this problem, we need to find the marked price of the cycle based on the given conditions of discount and profit.

### Problem Statement:
- The cost price of the cycle is ₹1440.
- The seller marks the price in such a way that after a 10% discount on the marked price, there is still a 15% profit on the cost price.
- We need to find the marked price.

### Solution:

1. **Determine the Selling Price with Profit:**

   - Given a 15% profit on the cost price:
   \[
   \text{Profit} = 15\% \text{ of } 1440 = \frac{15}{100} \times 1440 = 216
   \]

   - Therefore, the selling price after profit is:
   \[
   \text{Selling Price} = \text{Cost Price} + \text{Profit} = 1440 + 216 = 1656
   \]

2. **Consider the Discount:**

   - The selling price after a 10% discount on the marked price \( M \) is ₹1656.
   - The relationship between the marked price and selling price with a discount is given by:
   \[
   M - \left(\frac{10}{100} \times M\right) = 1656
   \]

   - Simplify the equation:
   \[
   0.9M = 1656
   \]

3. **Solve for the Marked Price \( M \):**

   - Divide both sides by 0.9:
   \[
   M = \frac{1656}{0.9}
   \]

   - Calculate:
   \[
   M = 1840
   \]

### Conclusion:
The marked price of the cycle is ₹1840.

### Additional Questions for Practice:

1. If the discount was 20% instead of 10%, what would the new marked price be for the same profit?
2. How would the selling price change if the profit margin was increased to 20%?
3. What is the break-even selling price (no profit or loss) for the cycle?
4. How do you calculate the percentage of discount given a marked price and a selling price?
5. If the cost price increases by 10%, what should be the new marked price to maintain the same profit margin after a 10% discount?
6. What is the impact on profit if the discount percentage is increased?
7. How can you calculate the marked price if only the cost price and desired profit percentage are known?
8. If a cycle was sold at a loss of 5%, what would be the selling price?

### Tip:
Always verify your calculations by checking that the final selling price (after discount) aligns with the intended profit percentage over the cost price. This ensures accuracy in solving such problems.

Learn how to calculate the marked price of an item given cost price, profit percentage, and discount percentage. This example problem covers essential concepts in profit and loss, discount calculations, and percentage formulas. Suitable for high school students.

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