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?

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Solution

Step 1. Declaring the variable x as multiple of ratios
We have given,
The Seats for Mathematics, Physics and Biology in a school are in the ratio $5 : 7 : 8$
Let the number of seats in Mathematics, Physics, and Biology be $5 x, 7 x$ and $8 x .$
Percentage of seats increase in Mathematics, Physics, and Biology are $40 %, 50 %$ and $75 %$
Step 2. Following the question statement.
Mathematics seats = $5 x + (40 % o f 5 x) = 5 x + 2 x = 7 x$
Physics seats = $7 x + (50 % o f 7 x) = 7 x + 3.5 x = 10.5 x$
Biology seats = $8 x + (75 % o f 8 x) = 8 x + 6 x = 14 x$
Ratio of increased seat
$= \frac{7 x}{7 x} : \frac{10.5 x}{7 x} : \frac{14 x}{7 x} = 1 : 1.5 : 2 = 2 : 3 : 4$
Hence, ratio of increased seats is $1 : 1.5 : 2 o r 2 : 3 : 4$ .

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