Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively, what will be the ratio of increased seats? 

Let the number of seats is =x
Given ratio in the question for mathematics, Physics and Biology =5:7:8
So, the number of seats for mathematics = 5x
The number of seats for Physics =7x
The number of seats for Biology =8x
There is proposal to increase the seats so, the number of seats after increasing the seats
$$\begin{gathered} \text{ Mathematics }=5x+5x\times 40\mathrm{\%} \\ \begin{array}{l}\Rightarrow 5\mathrm{x}+5\mathrm{x}\times \frac{40}{100}\\ \Rightarrow 5\mathrm{x}+2\mathrm{x}\\ =7\mathrm{x} \\ \end{array} \end{gathered}$$
$\begin{array}{l}\text{ Physics }=7x+7x\times 50\mathrm{\%}\\ \Rightarrow 7x+7x\times \frac{50}{100}\\ \Rightarrow 7x+3.5x\\ =10.5x\end{array}$
$\begin{array}{l}\text{ Biology }=8x+8x\times 75\mathrm{\%}\\ \Rightarrow 8x+8x\times \frac{75}{100}\\ \Rightarrow 8x+6x\\ =14x\end{array}$
Here new ratio for seats of mathematic, Physics and Biology
=7x:10.5x:14x
After simplifying the ratio, we get
=$1:1.5:2$
=$2:3:4$