In a bag full of pencils, $$\frac{3}{4}$$​of the pencils were coloured pencils, and $$\frac{8}{15}$$​of the coloured pencils were red. If there were 40 red pencils in the bag, what was the total number of pencils in the bag?

Correct option is A

Given:

- Fraction of coloured pencils = 3/4

- Fraction of red pencils in coloured pencils = 8/15

- Number of red pencils = 40

- Total pencils = x

Formula Used:

Number of red pencils = Total pencils × Fraction of coloured pencils × Fraction of red pencils

Solution:

​$$\begin{aligned}&40 = x \times \frac{3}{4} \times \frac{8}{15} \\\ \\&\frac{3}{4} \times \frac{8}{15} = \frac{24}{60} = \frac{2}{5} \\\ \\&40 = x \times \frac{2}{5} \\\ \\&200 = 2x \\\ \\&x = 100\end{aligned}$$​​

The total number of pencils in the bag was 100.