Ratios & Proportion

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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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Option(A) is correct

Originally, let the number of seats for Mathematics, Physics and Biology be $5x$, $7x$ and $8x$ respectively.

Number of increased seats are ($140\%$ of $5x$), ($150\%$ of $7x$) and ($175\%$ of $8x$).

\(\begin{align*} \Rightarrow & \left(\dfrac{140}{100}\times 5x\right), \left(\dfrac{150}{100}\times 7x\right), \left(\dfrac{175}{100}\times 8x\right)\\ \Rightarrow & 7x, \dfrac{21x}{2},14x\\ \text{The required ratio}&=7x:\dfrac{21x}{2}:14x\\ &=14x:21x:28x\\ &=2:3:4 \end{align*}\)

Edit: Thank you LAKSHMAN for pointing out typo in the question. Corrected it.

Edit 2: For an alternative solution, check comment by Sravan Reddy.

(4) Comment(s)

Sravan Reddy

Take some numbers. I usually multiply ratios with with 10 - so 50,70,80

40% increase in 50 = 70

50% increase in 70 = 105

75% increase in 80 = 140

So, ratio is 2:3:4

P.S. Use this only if you are quick and comfortable with numbers


Question is given in such a way that seats are increased by numbers but answers were solved considering that those are increased by percentages.Kindly modify it


Thank you for pointing out, corrected.


why have we used 140 , 150 and 175 ? why always use 100?? why not only 40 ,50 and 75 ?pls explain.