Question

If $\frac{1}{8}$ of a pencil is black, $\frac{1}{2}$ of the remaining is white and the remaining $3\frac{1}{2}$ cm is blue, find the total length of the pencil.

• A. 8 cm
• B. 10 cm
• C. 7 cm
• D. 6 cm

Answer 1

The correct option is A 8 cm

Let's assume length of the pencil is $x$
As per question, portion(length) of black in pencil $=\frac{x}{8}$

Remaining portion $=x-\frac{x}{8}=\frac{7x}{8}$

So, White portion $=\frac{1}{2}\times \frac{7x}{8}=\frac{7x}{16}$

So, remaining portion $=\frac{7x}{8}-\frac{7x}{16}=\frac{7x}{16}$

As per question,
$\frac{7x}{16}=3.5$
$x=8$ cm