Question

The following pie chart represents the expenses of Jack on various items.
Find the ratio of central angle made by the food sector to the clothing sector?

• A. $\frac{1}{2}$
• B. $4$
• C. $\frac{1}{3}$
• D. $\frac{1}{4}$

Answer 1

The correct option is D $\frac{1}{4}$

Percentage of the food sector out of the total sectors $=10\%$
Percentage of the clothing sector out of the total sectors $=40\%$

In a pie chart, the total angle at the centre of the circle is ${360}^{\circ }.$

$\therefore$ Central angle made by the food sector $=10\%$ of ${360}^{\circ }$
$=10\%\times {360}^{\circ }$
$=\frac{10}{100}\times {360}^{\circ }$
$=\frac{1}{10}\times {360}^{\circ }$
$={36}^{\circ }$

$\therefore$ Central angle made by the clothing sector $=40\%$ of ${360}^{\circ }$
$=40\%\times {360}^{\circ }$
$=\frac{40}{100}\times {360}^{\circ }$
$=\frac{2}{5}\times {360}^{\circ }$
$={144}^{\circ }$

Ratio of central angle made by the food sector to the clothing sector
$=\frac{{36}^{\circ }}{{144}^{\circ }}$
$=\frac{1}{4}$

Option (d.) is the correct choice.