Directions: The following pie diagram shows the marks obtained by Raju in his tenth class examinations, with a total of 554 marks. The values mentioned on the pie diagram are the central angles, in degrees, corresponding to each subject.
The subjects and their corresponding central angles, as read from the chart, are: 1st Language = 90°, Hindi = 60°, English = 63°, Mathematics = 72°, Science = 75°, Social = 80°.
The subject in which he scored \(16\frac{2}{3}\%\) of the marks is:
Show Hint
Convert 16 2/3% into a simple fraction of 360 degrees, then match that angle to the chart's labelled slices.
On a pie chart, the fraction of the total that any slice represents is simply that slice's central angle divided by 360° (this is the standard convention used to read such degree-labelled pie charts, and it is what the chart's own figures are built on).
We are told a subject accounts for \(16\frac{2}{3}\%\) of the marks. Writing this as a fraction, \(16\frac{2}{3}\% = \frac{50}{3}\% = \frac{50}{300} = \frac{1}{6}\).
So we need the subject whose central angle divided by 360° equals \(\frac{1}{6}\), which means the angle itself is \(\frac{360}{6} = 60^\circ\).
Looking at the chart, the slice marked 60° belongs to Hindi.
As a check, computing the marks directly: Hindi's marks \(= \frac{60}{360}\times 554 = \frac{554}{6} \approx 92.33\). And \(16\frac{2}{3}\%\) of 554 is \(\frac{50}{300}\times 554 = \frac{554}{6}\approx 92.33\) as well, confirming the match.
