Question

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?
A) 2:3:4
B) 6:7:8
C) 6:8:9
D) None of these

Answer 1

Hint: The question is related to ratio and proportion. First find the increased number of seats by the given percentage in the question. Let the actual number of seats for mathematics, Physics and Biology is $x$.

Complete step by step answer:
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
Mathematics =$5x + 5x \times 40\% $
$ \Rightarrow 5x + 5x \times \dfrac{{40}}{{100}}$
$ \Rightarrow 5x + 2x$
$ = 7x$
Physics =$7x + 7x \times 50\% $
$ \Rightarrow 7x + 7x \times \dfrac{{50}}{{100}}$
$ \Rightarrow 7x + 3.5x$
$ = 10.5x$
Biology =$8x + 8x \times 75\% $
$ \Rightarrow 8x + 8x \times \dfrac{{75}}{{100}}$
$ \Rightarrow 8x + 6x$
$ = 14x$
Here new ratio for seats of mathematic, Physics and Biology
=\[7x:10.5x:14x\]
After simplifying the ratio, we get
=$1:1.5:2$
Multiply the ratio by
=$2:3:4$
Hence the ratio of increased seats is
$\therefore 2:3:4$

Therefore, option A is correct.

Note:
Here in this question students do the mistake in the last part of the solution as there is no option in the question which contains the ratio $1:1.5:2$, so they mark the option D which is incorrect. You have to multiply the ratio by 2 for getting your final answer. As the question mentioned that the number of seats increased by the given percentage, you have to solve the percentage and add it into the given number of ratios.