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Let's break down the problem step by step:

1. **Initial Investment in Scheme M:**
   - Manish invested ₹60,000 in scheme M, which offers a simple interest of 25% per annum.
   - The investment was for 4 years.

   Using the simple interest formula \( SI = P \times R \times T \), where \( P \) is the principal (₹60,000), \( R \) is the rate (25% or 0.25), and \( T \) is time (4 years):
   \[
   SI = 60000 \times 0.25 \times 4 = 60000 \times 1 = ₹60,000
   \]
   The total amount in scheme M after 4 years is:
   \[
   A = P + SI = 60000 + 60000 = ₹120,000
   \]
   So, \( x = ₹120,000 \), which is the amount withdrawn after 4 years.

2. **Investment in Scheme N:**
   - The ₹120,000 is then invested in scheme N, which offers 40% compounded annually.
   - After 3 years, the amount from scheme N is ₹14,700 more than the amount from scheme M (₹120,000).

   Using the compound interest formula \( A = P \times \left(1 + \frac{R}{100}\right)^T \), where \( P = ₹120,000 \), \( R = 40% \), and \( T = 3 \):
   \[
   A = 120000 \times \left(1 + \frac{40}{100}\right)^3 = 120000 \times \left(1.4\right)^3
   \]
   Let's calculate this step by step:
   \[
   1.4^3 = 2.744
   \]
   \[
   A = 120000 \times 2.744 = ₹329,280
   \]
   So, the amount in scheme N after 3 years is ₹329,280.

3. **Amount from Scheme N and the Difference:**
   - The difference between the amount received from scheme N and the amount received from scheme M is ₹14,700.
   \[
   329,280 - 120,000 = ₹209,280
   \]
   However, it says that the difference is ₹14,700. This implies that the additional amount from scheme N after 3 years is more than the amount he initially had in scheme M.

4. **Final Calculation (38% of \( x - 500 \)):**
   Now we need to find the value of 38% of \( x - 500 \), where \( x = 120,000 \):
   \[
   x - 500 = 120000 - 500 = ₹119,500
   \]
   38% of ₹119,500 is:
   \[
   0.38 \times 119500 = ₹45,410
   \]

Thus, the value of 38% of \( x - 500 \) is **₹45,410**, but since this is not an option in the given choices, we might need to recheck with additional information or conditions from the question.

Would you like more details on any step or further clarification?

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Here are five follow-up questions related to this problem:
1. What is the effect of compounding frequency in scheme N on the total amount?
2. How does simple interest differ from compound interest in long-term investments?
3. What would be the total amount if the interest in scheme N was compounded quarterly?
4. How would the results change if Manish had invested in scheme N first, before scheme M?
5. What is the formula for calculating effective interest rate when dealing with compounded interest?

**Tip:** When working with both simple and compound interest, always distinguish the compounding frequency for accurate results!

Manish invested Rs 60000 in scheme 'M' that offers simple interest at 25% per annum. Four years later, he withdrew Rs 'x' from scheme 'M' and invested it in scheme 'N' that offers compound interest of 40% per annum compounded annually. If three years after investing his sum in scheme 'N,' the amount received from scheme 'N' was Rs 14700 more than that from scheme 'M', then find the value of 38% of (x - 500).

Learn how to solve a complex investment problem involving both simple and compound interest rates. Manish's investments in schemes 'M' and 'N' involve calculations for 25% simple interest and 40% compound interest per annum. Suitable for students in Grades 9-12.

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