Seats of Physics, Chemistry and Mathematics in a school are in the ratio 4 : 5 : 6. There is a proposal to increase these seats by 75 in each department. What were the total number of seats in the school finally?

Options

A. 600
B. 750
C. 900
D. Data insufficient

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the Ratios
The seats of Physics, Chemistry, and Mathematics are given in the ratio of 4:5:6. This means that for every 4 seats in Physics, there are 5 in Chemistry and 6 in Mathematics.

### Step 2: Assign Variables
Let the number of seats in each subject be represented as follows:
- Physics seats = 4x
- Chemistry seats = 5x
- Mathematics seats = 6x

### Step 3: Calculate the Total Seats Before Increase
The total number of seats before the increase can be calculated by adding the seats in each subject:
\[ \text{Total seats} = 4x + 5x + 6x = 15x \]

### Step 4: Increase the Seats
According to the problem, there is a proposal to increase the seats by 75 in each department. Therefore, the new number of seats will be:
- New Physics seats = \(4x + 75\)
- New Chemistry seats = \(5x + 75\)
- New Mathematics seats = \(6x + 75\)

### Step 5: Calculate the Total Seats After Increase
Now, we can calculate the total number of seats after the increase:
\[ \text{Total seats after increase} = (4x + 75) + (5x + 75) + (6x + 75) \]
Combining the terms:
\[ = 4x + 5x + 6x + 75 + 75 + 75 \]
\[ = 15x + 225 \]

### Step 6: Conclusion
The total number of seats in the school after the increase is \(15x + 225\). However, we need the value of \(x\) to find the exact number of seats. Since \(x\) is not provided in the problem, we can conclude that the total number of seats is expressed in terms of \(x\).

### Final Answer
The total number of seats in the school after the increase is \(15x + 225\).

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