The ratio of students in a coaching preparing for B.Tech and MBA is 4 : 5. The ratio of fees collected from each of B.Tech and MBA student is 25: 16. If the total amount collected from all the students is 1.62 lakh, what is the total amount collected from only MBA aspirants?

Options

A. ₹ 62000
B. ₹ 72000
C. ₹ 80000
D. none of these

Answer

To solve the problem step by step, we will follow the given ratios and the total amount collected.

### Step 1: Understand the Ratios
We are given:
- The ratio of students preparing for B.Tech to MBA is 4:5.
- The ratio of fees collected from each B.Tech student to each MBA student is 25:16.

### Step 2: Assign Variables
Let:
- The number of B.Tech students be \( 4x \).
- The number of MBA students be \( 5x \).

### Step 3: Calculate Total Students
The total number of students is:
\[ \text{Total Students} = 4x + 5x = 9x \]

### Step 4: Assign Fees
Let:
- The fee collected from each B.Tech student be \( 25y \).
- The fee collected from each MBA student be \( 16y \).

### Step 5: Calculate Total Fees Collected
The total fees collected from all students is:
\[ \text{Total Fees} = (\text{Number of B.Tech Students} \times \text{Fee per B.Tech Student}) + (\text{Number of MBA Students} \times \text{Fee per MBA Student}) \]
\[ = (4x \times 25y) + (5x \times 16y) \]
\[ = 100xy + 80xy = 180xy \]

### Step 6: Set Up the Equation
We know the total amount collected is 1.62 lakh (or 162000):
\[ 180xy = 162000 \]

### Step 7: Solve for \( xy \)
To find \( xy \):
\[ xy = \frac{162000}{180} = 900 \]

### Step 8: Calculate the Amount Collected from MBA Students
Now, we need to find the total amount collected from only MBA aspirants:
\[ \text{Total Fees from MBA Students} = \text{Number of MBA Students} \times \text{Fee per MBA Student} \]
\[ = 5x \times 16y \]
\[ = 80xy \]
Substituting \( xy = 900 \):
\[ = 80 \times 900 = 72000 \]

### Final Answer
The total amount collected from only MBA aspirants is **72000**.

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