Initial Seat Ratio

The initial number of seats for Mathematics, Physics, and Biology are in the ratio 2:3:4.

Understanding Percentage Increase on Ratios

When each component of a ratio is increased by the same percentage, the ratio itself does not change. This is because the increase acts as a common multiplier for all parts of the ratio.

Let the initial number of seats be $2x$, $3x$, and $4x$ for Mathematics, Physics, and Biology, respectively. A 50% increase means multiplying each quantity by $1 + 0.50 = 1.5$.

• New Mathematics seats: $2x \times 1.5 = 3x$
• New Physics seats: $3x \times 1.5 = 4.5x$
• New Biology seats: $4x \times 1.5 = 6x$

Calculating the New Ratio

The new ratio is $3x : 4.5x : 6x$. To simplify this ratio, we can divide each term by $x$: $3 : 4.5 : 6$ To eliminate the decimal, multiply each part by 2: $3 \times 2 : 4.5 \times 2 : 6 \times 2$ $6 : 9 : 12$ Now, divide each part by their greatest common divisor, which is 3: $6 \div 3 : 9 \div 3 : 12 \div 3$ $2 : 3 : 4$ Alternatively, we can observe that the new ratio is $(2 \times 1.5) : (3 \times 1.5) : (4 \times 1.5)$. Since $1.5$ is a common factor, it can be cancelled out, leaving the original ratio $2:3:4$.

Final Ratio Conclusion

The respective ratio of seats for Mathematics, Physics, and Biology remains 2:3:4 after a 50% increase in each.