A pie chart gives the expenditure on five different items A, B, C, D and E in a household. If B, C, D and E correspond to 90º, 50º, 45º and 75º respectively, then what is the percentage of expenditure on item A?

Correct Option (4)

A pie chart represents the total expenditure as 360°. The given expenditures for items B, C, D, and E are 90°, 50°, 45°, and 75° respectively.

First, calculate the sum of the angles for items B, C, D, and E:

$$90{}^{\circ }+50{}^{\circ }+45{}^{\circ }+75{}^{\circ }=260{}^{\circ }$$

The angle corresponding to the expenditure on item A is determined by subtracting this sum from the total angle of the pie chart:

$$\text{Angle for A}=360{}^{\circ }-260{}^{\circ }=100{}^{\circ }$$

To find the percentage of expenditure on item A, divide the angle for A by the total angle (360°) and multiply by 100:

$$\text{Percentage of expenditure on A}=\frac{100{}^{\circ }}{360{}^{\circ }}\times 100$$

$$=\frac{10}{36}\times 100$$

$$=\frac{5}{18}\times 100$$

$$=\frac{500}{18}=\frac{250}{9}$$

Incorrect Options:

Options 1, 2, and 3 do not represent the correct percentage of expenditure on item A. These values would result from miscalculations in summing the angles, determining the angle for item A, or converting the angle to a percentage of the total expenditure.