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 90°, 50°, 45° and 75° respectively, then what is the percentage of expenditure on item A?

The correct option is:
$\frac{250}{9}$

Step-by-step Explanation:

1. Understand the properties of a pie chart:
A pie chart represents the division of a whole into different sectors. The total angle of a circle is 360°, which corresponds to 100% of the total expenditure.

2. Find the sum of the angles for items B, C, D, and E:
We are given the central angles for four of the five items:
• Item B = 90°
• Item C = 50°
• Item D = 45°
• Item E = 75°

The sum of these angles is:
90° + 50° + 45° + 75° = 260°

3. Calculate the central angle corresponding to item A:
Since the total sum of all central angles in the pie chart must be 360°:
Angle for A = 360° - 260° = 100°

4. Determine the percentage of expenditure on item A:
To convert the angle for item A into a percentage of the total expenditure, we divide the angle for A by the total angle of the circle (360°) and multiply by 100:

Percentage for A = $\frac{100}{360}\times 100$

Let us simplify this expression step-by-step:

Percentage for A =

Percentage for A = $\frac{5}{18}\times 100$

Percentage for A = $\frac{500}{18}$

Percentage for A = $\frac{250}{9}$