An outgoing batch of students wants to gift a PA system worth Rs `4,200.` to their school. If the teachers, offer to pay `50%` more than the students and an external benefactor gives three time the teacher's contribution, then how much should the teachers donate?

Options

A. Rs 600
B. Rs 840
C. Rs 900
D. Rs 1,200

Answer

To solve the problem step by step, we need to define the contributions of the students, teachers, and the external benefactor.

### Step 1: Define the variables
Let the contribution of the students be denoted as \( S \).

### Step 2: Calculate the teachers' contribution
According to the problem, the teachers contribute 50% more than the students. Therefore, the teachers' contribution \( T \) can be expressed as:
\[ T = S + 0.5S = 1.5S \]

### Step 3: Calculate the external benefactor's contribution
The external benefactor contributes three times the teachers' contribution. Thus, the benefactor's contribution \( B \) is:
\[ B = 3T = 3(1.5S) = 4.5S \]

### Step 4: Set up the equation for total contributions
The total contribution from students, teachers, and the external benefactor must equal the cost of the PA system, which is Rs. 4200. Therefore, we can write the equation:
\[ S + T + B = 4200 \]
Substituting the expressions for \( T \) and \( B \):
\[ S + 1.5S + 4.5S = 4200 \]

### Step 5: Combine like terms
Combining the contributions gives:
\[ S + 1.5S + 4.5S = 7S \]
Thus, we have:
\[ 7S = 4200 \]

### Step 6: Solve for \( S \)
To find the students' contribution \( S \), divide both sides by 7:
\[ S = \frac{4200}{7} = 600 \]

### Step 7: Calculate the teachers' contribution
Now that we have \( S \), we can find the teachers' contribution \( T \):
\[ T = 1.5S = 1.5 \times 600 = 900 \]

### Conclusion
The teachers should donate Rs. 900.

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