Aptitude Discussion

Q. |
In a library, $20\%$ of the books are in Hindi. $50\%$ of the remaining are in English and $30\%$ of the remaining are in French. The remaining $6,300$ books are in regional languages. What is the total number of books in library? |

✖ A. |
19,500 |

✖ B. |
20,500 |

✖ C. |
21,500 |

✔ D. |
22,500 |

**Solution:**

Option(**D**) is correct

Let the total number of books in the library be $x$.

$20\%$ of these books are in Hindi $= 0.2x$ books in Hindi.

Therefore the remaining books $= x - 0.2x = 0.8x$ books.

$50\%$ of these remaining books are in English $= 50\% \text{ of } 0.8x = 0.4x$ books.

Therefore the remaining books $= 0.8x - 0.4x = 0.4x$ books.

$30\%$ of these remaining books are in French $= 30\% \text{ of } 0.4x = 0.12x$ books.

Now the remaining books $= 0.4x - 0.12x = 0.28x$ books.

According to the question the total remaining books $= 6300$.

$\Rightarrow 0.28x=6300$

$\Rightarrow x = \dfrac{6300}{0.28}$

$\Rightarrow x = 22,500 \text{ books.}$

Hence, the total number of books in the library $= \textbf{22,500 books.}$

**Zoha Amjad**

*()
*

total books * 80% * 50% * 70% = 6300

total books = 22500