Question

If one-eight of a pencil is black, half of the remaining is yellow ,and the remaining $3\frac{1}{2}$cm
is blue ;then what is the total length of the pencil ?

• A. $6$cm
• B. $7$cm
• C. $8$cm
• D. $11$cm

Answer 1

The correct option is C $8$cm

$\frac{1}{8}$ th part of the pencil is black
$\Rightarrow$ Remaining part of the pencil = $1-\frac{1}{8}=\frac{7}{8}$
$\therefore$ part of pencil that is yellow
= $\frac{1}{2}$ of remaining $=\frac{1}{2}\times \frac{7}{8}=\frac{7}{16}$
Now part left that is blue
$=1-(\frac{1}{8}+\frac{7}{16})=1-\frac{9}{16}=\frac{7}{16}$
Since it is given that 3.5 cm of the pencil is blue
$\frac{7}{16}$ of total length = 3.5 cm
$\Rightarrow$ Total length $=\frac{16}{7}\times 3.5cm=8cm$