Question

In a class, $\frac{1}{10}$th of the class' kids have pens while $\frac{4}{5}$th have pencils. But no one has both. What fraction of kids neither have a pen or pencil?

• A. $\frac{7}{10}$
• B. $\frac{1}{10}$
• C. $\frac{9}{10}$
• D. $\frac{3}{5}$

Answer 1

The correct option is B

$\frac{1}{10}$

Fraction of children with pens = $\frac{1}{10}$
Fraction of children with pencils = $\frac{4}{5}$
Fraction of children having either a pen or a pencil $=\frac{1}{10}+\frac{4}{5}$

LCM of 10 and 5 is 10.
$\frac{1}{10}+\frac{4}{5}$ $=\frac{1}{10}+\frac{4\times 2}{5\times 2}=\frac{1}{10}+\frac{8}{10}=\frac{1+8}{!0}=\frac{9}{10}$

Fraction of kids who neither have pen or pencil = 1 - Fraction of kids who either have pen or pencil
$=1-\frac{9}{10}=\frac{1\times 10}{1\times 10}-\frac{9}{10}=\frac{10-9}{10}=\frac{1}{10}$

$\therefore$ Fraction of kids who neither have pen or pencil is $\frac{1}{10}$.