Aptitude Discussion

Q. |
The ratio of the number of boys and girls in a college is $7:8$. If the percentage increase in the number of boys and girls be $20\%$ and $10\%$ respectively, what will be the new ratio? |

✖ A. |
$8:9$ |

✖ B. |
$17:18$ |

✔ C. |
$21:22$ |

✖ D. |
Cannot be determined |

**Solution:**

Option(**C**) is correct

Originally, let the number of boys and girls in the college be $7x$ and $8x$ respectively.

Their increased number is ($120\%$ of $7x$) and ($110\%$ of $8x$).

\(\begin{align*} \Rightarrow & \left(\dfrac{120}{100}\times 7x\right)\text{ and }\left(\dfrac{110}{100}\times 8x\right)\\ \Rightarrow & \dfrac{42x}{5}\text{and}\dfrac{44x}{5} \end{align*}\)

So, the required ratio = \(\left( \dfrac{42x}{5}:\dfrac{44x}{5}\right)=21:22\)

**Edit:** Thank you, **Anurag**, corrected the typo.

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

**Sravan Reddy**

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**Anurag**

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I think the question needs to be modified. Increase in number of boys and girls should be given in the form of percentage instead of numbers only.

Thank you for letting me know, corrected it.

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

20% increase in 70 = 84

10% increase in 80 = 88

So, ratio is 21:22

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