2:3:4
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.
Important Questions from Ratio and Proportion (Notes)
- Anand and Deepak started a business investing ₹ 22,500 and ₹ 35,000 respectively. Out of a total profit of ₹ 13,800, Deepak's share is
- If A exceeds B by 50% and B is less than C by 25%, then A: C is:
- A, B and C invested some money in the ratio of 3 : 2 : K. If C's share is Rs 120 more than A's share, B's share is Rs 30 less than A's share, then the value of K is :
- For any two numbers p and q,
$(p + q) : (p - q) : pq = 7 : 1 : 60$
If $p^2 + q^2 = r^2$, then r is equal to - If A : B = 5 : 6 and B : C = 6 : 7, then A + B : B + C : A + C is :
