Directions : Read the following pie charts carefully and answer the questions…
2022
Directions : Read the following pie charts carefully and answer the questions given below.
Pie charts (i) shows percentage distribution of runs scored by three (P, Q & R) different batsmen in a match and pie chart (ii) shows percentage distribution of balls faced by each batsman in a match.
Note: (I) Strike rate of P is 25.
(II) Balls faced by Q is 180 and his strike rate is 33 ⅓.
(III) Had P faced the same number of balls Q faced, but scored same number of runs as he scored initially, then his strike rate would have been double that of Q.
(IV) Balls faced by R is half of the balls faced by P.
(V) Strike rate = (Total runs scored / Total balls faced) × 100.
(VI) Central angle of runs scored by R is 198°.
Find the difference between the central angle of runs scored by P and the central angle of balls faced by Q.
- A.
36°
- B.
48°
- C.
18°
- D.
54°
- E.
12°
Show answer & explanation
Correct answer: A
Concept
In a pie chart, the central angle of any category is directly proportional to its share of the total: central angle = (category value ÷ total) × 360°. Here two independent totals exist — total runs and total balls — each forming its own 360° pie. Strike rate links the two quantities: Strike Rate = (Runs ÷ Balls) × 100. So the method is to recover each batsman's actual runs and balls from the notes, then convert the required shares into angles.
Working
Runs of Q. Q faced 180 balls at strike rate 100/3, so Runs of Q = (100/3 ÷ 100) × 180 = 60 runs.
Runs of P (Note III). If P had faced 180 balls keeping the same runs, his strike rate would be double Q's = 2 × 100/3 = 200/3. So (Runs of P ÷ 180) × 100 = 200/3 ⇒ Runs of P = (200/3 ÷ 100) × 180 = 120 runs.
Balls of P (Note I). P's actual strike rate is 25, so (120 ÷ Balls of P) × 100 = 25 ⇒ Balls of P = 120 × 100 ÷ 25 = 480 balls. By Note IV, Balls of R = 480 ÷ 2 = 240 balls.
Total runs (Note VI). R's runs make a 198° angle, i.e. 198 ÷ 360 = 55% of total runs. Then P and Q together are 45% of runs, and they scored 120 + 60 = 180 runs. So total runs = 180 ÷ 0.45 = 400.
Central angle of P's runs. P's runs = 120 out of 400 = 30%, so the angle = 0.30 × 360 = 108°.
Central angle of Q's balls. Total balls = 480 + 180 + 240 = 900. Q's balls = 180 out of 900 = 20%, so the angle = 0.20 × 360 = 72°.
Required difference. 108° − 72° = 36°.
Cross-check
The runs pie closes: R = 220 (55% → 198°), P = 120 (30% → 108°), Q = 60 (15% → 54°); 198 + 108 + 54 = 360°. The balls pie also closes: P = 480 (53.33% → 192°), Q = 180 (20% → 72°), R = 240 (26.67% → 96°); 192 + 72 + 96 = 360°. The two angles asked for are 108° and 72°, differing by 36°.