Question

Which of the following options is CORRECT for the fraction of shaded parts in figures $I$ and $II$?

• A. $I>II$
• B. $II>I$
• C. $I=II$
• D. Can't be determined

Answer 1

Answer: (A)

$I>II$

Number of equal parts in Figure $I=24$
Number of shaded parts in Figure $I=20$
$\therefore$ Required shaded fraction for figure $I=\frac{20}{24}=\frac{5}{6}$
Number of equal parts in figure $II=40$
Number of shaded parts in figure $II=32$
$\therefore$ Required shaded fraction for figure $II=\frac{32}{40}=\frac{4}{5}$
Now, $\frac{5}{6}=\frac{5\times 5}{6\times 5}=\frac{25}{30}$

and $\frac{4}{5}=\frac{4\times 6}{5\times 6}=\frac{24}{30}$

$\because \frac{25}{30}>\frac{24}{30}$

$\therefore I>II$.