Aptitude Discussion

Q. |
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 |

**Solution:**

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.**

**Sravan Reddy**

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**LAKSHMAN**

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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.

**Sjain**

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

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