`3650` is divided among 4 engineers, 3 MBAs and 5 CAs such that 3 CAs get as much as 2 MBAs and 3 Engineers as much as 2 CAs. Find the share of an MBA.

Options

A. 300
B. 450
C. 475
D. None of these

Answer

To solve the problem of dividing the amount of 3650 among 4 engineers, 3 MBAs, and 5 CAs based on the given conditions, we can follow these steps:

### Step-by-Step Solution:

1. **Define Variables:**
- Let the share of an engineer be \( E \).
- Let the share of an MBA be \( M \).
- Let the share of a CA be \( C \).

2. **Set Up the Total Amount Equation:**
- The total amount distributed is given by:
\[ 4E + 3M + 5C = 3650 \]

3. **Use the Given Relationships:**
- From the problem, we know:
- 3 CAs get as much as 2 MBAs:
\[ 3C = 2M \implies C = \frac{2}{3}M \]
- 3 Engineers get as much as 2 CAs:
\[ 3E = 2C \implies E = \frac{2}{3}C \]

4. **Substitute \( C \) in terms of \( M \) into \( E \):**
- Substitute \( C = \frac{2}{3}M \) into \( E \):
\[ E = \frac{2}{3} \left(\frac{2}{3}M\right) = \frac{4}{9}M \]

5. **Substitute \( E \) and \( C \) back into the total amount equation:**
- Now substitute \( E \) and \( C \) into the total amount equation:
\[ 4E + 3M + 5C = 3650 \]
\[ 4\left(\frac{4}{9}M\right) + 3M + 5\left(\frac{2}{3}M\right) = 3650 \]
\[ \frac{16}{9}M + 3M + \frac{10}{3}M = 3650 \]

6. **Convert all terms to a common denominator:**
- The common denominator for 9, 1, and 3 is 9:
\[ \frac{16}{9}M + \frac{27}{9}M + \frac{30}{9}M = 3650 \]
\[ \frac{16 + 27 + 30}{9}M = 3650 \]
\[ \frac{73}{9}M = 3650 \]

7. **Solve for \( M \):**
- Multiply both sides by 9:
\[ 73M = 3650 \times 9 \]
\[ M = \frac{3650 \times 9}{73} \]
- Calculate \( 3650 \times 9 = 32850 \):
\[ M = \frac{32850}{73} = 450 \]

8. **Conclusion:**
- The share of an MBA is \( M = 450 \).

### Final Answer:
The share of an MBA is **450**.