Question

Question 8 :

Asha and Samuel have bookshelves of the same size partly filled with books. Asha’s shelf is $\frac{5}{6}$th full and Samuel’s shelf is $\frac{2}{5}$ th full. Whose bookshelf is more full? By what fraction?

Answer 1

As per the question

Asha and Samuel have bookshelves of the same size.

Asha’s shelf is $\frac{5}{6}$th full.

Samuel’s shelf is $\frac{2}{5}$ th full.

We have to find out whose bookshelf is more full. Now, it is given that the bookshelves of both Asha and Samuel have the same size.

So to calculate whose whose bookshelf is more full we have to find which fraction among $\frac{5}{6}$ and $\frac{2}{5}$ is greater.

$\frac{5}{6}=\frac{5}{6}\times \frac{5}{5}=\frac{25}{30}$ and $\frac{2}{5}=\frac{2}{5}\times \frac{6}{6}=\frac{12}{30}$.

[$\because$ L.C.M. of 6 and 5 is 30 ]

$\therefore \frac{25}{30}>\frac{12}{30}$

$\Rightarrow \frac{5}{6}>\frac{2}{5}$

$\therefore$ Asha's bookshelf is more covered than Samuel.

To calculate by what fraction is the bookshelf is more full, we should calculate the difference between the two fractions.

The fraction by which Asha's bookshelf covered is more than Samuel's is = $\frac{5}{6}-\frac{2}{5}=\frac{25}{30}-\frac{12}{30}=\frac{13}{30}$