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?

(a) 112/9
(b) 125/6
(c) 155/9
(d) 250/9 ✓ UPSC's answer

Why the answer is (d)

• The total angle of a pie chart is 360 degrees.

• The sum of the angles for items B, C, D, and E is 90 + 50 + 45 + 75 = 260 degrees.

• The angle corresponding to item A is 360 - 260 = 100 degrees.

• The percentage of expenditure on item A is calculated as (100 / 360) * 100.

• Simplifying the fraction 10000 / 360 gives 1000 / 36, which reduces to 250 / 9.

• Therefore, the correct percentage is 250/9, which corresponds to option (d).

Why the other options are wrong

(a) 112/9: 112/9 is approximately 12.44%, which does not match the calculated 27.78% (250/9).
(b) 125/6: 125/6 is approximately 20.83%, which is incorrect as the angle for A is 100 degrees, not 75 degrees.
(c) 155/9: 155/9 is approximately 17.22%, which does not correspond to the 100-degree sector of the pie chart.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2022, held on 5 June 2022. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.