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)
- If A exceeds B by 50% and B is less than C by 25%, then A: C 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 :
- The height of a tree varies as the square root of its age. When the age of the tree is 324 years, its height is 19 feet. What will be the height of the tree (in feet) at the age of 81 years?
When x is added to each of 13, 19, 16 and 23, then the numbers so obtained, in this order, are in proportion. Then, if $5x : y :: y : (8x-4)$, and $y > 0$, what is the value of y?
