Ananda has a library. $\frac{1}{6}$ of the books are children's story books, and $\frac{1}{4}$ are literature books. Ananda donated these books. The number of donated books is 150. We need to find: (i) The fraction of the total number of books that were donated. (ii) The total number of books originally in the library. (iii) The fraction of the total number of books that were given to a neighbour, given that Ananda gave 60 books to the neighbour. (iv) The fraction of the total number of books that were sold, given that Ananda sold $\frac{3}{5}$ of the remaining books after giving some to the neighbour.

1. Problem Description

Ananda has a library. $\frac{1}{6}$ of the books are children's story books, and $\frac{1}{4}$ are literature books. Ananda donated these books. The number of donated books is

1

5

0. We need to find:

(i) The fraction of the total number of books that were donated.

(ii) The total number of books originally in the library.

(iii) The fraction of the total number of books that were given to a neighbour, given that Ananda gave 60 books to the neighbour.

(iv) The fraction of the total number of books that were sold, given that Ananda sold $\frac{3}{5}$ of the remaining books after giving some to the neighbour.

2. Solution Steps

(i) Let $x$ be the total number of books in the library. The fraction of donated books is the sum of the fractions of children's story books and literature books:

$\frac{1}{6} + \frac{1}{4}$

To add the fractions, we need a common denominator, which is 12:

$\frac{1}{6} + \frac{1}{4} = \frac{2}{12} + \frac{3}{12} = \frac{5}{12}$

So, the fraction of donated books is $\frac{5}{12}$.

(ii) The number of donated books is 150, and this represents $\frac{5}{12}$ of the total number of books. We can set up the equation:

$\frac{5}{12}x = 150$

To solve for $x$, we multiply both sides by $\frac{12}{5}$:

$x = 150 \cdot \frac{12}{5} = \frac{150 \cdot 12}{5} = 30 \cdot 12 = 360$

So, the total number of books originally in the library is

3

6

0.

(iii) Ananda gave 60 books to a neighbour. We need to find what fraction of the total number of books this represents. The total number of books is

3

6

0. Fraction given to neighbour = $\frac{60}{360} = \frac{6}{36} = \frac{1}{6}$

So, the fraction of books given to the neighbour is $\frac{1}{6}$.

(iv) After giving 60 books to the neighbour, Ananda sold $\frac{3}{5}$ of the remaining books. The number of remaining books after the donation is $360 - 150 = 210$. After giving 60 books to the neighbour, the number of remaining books is $210 - 60 = 150$. Ananda sold $\frac{3}{5}$ of these 150 books.

Number of books sold = $\frac{3}{5} \cdot 150 = 3 \cdot 30 = 90$

We want to find the fraction of the total number of books (360) that were sold (90).

Fraction of books sold = $\frac{90}{360} = \frac{9}{36} = \frac{1}{4}$

So, the fraction of the total number of books that were sold is $\frac{1}{4}$.

3. Final Answer

(i) $\frac{5}{12}$

(ii) 360

(iii) $\frac{1}{6}$

(iv) $\frac{1}{4}$