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°.
If R scored his runs in only 6’s & 4’s and he hit 25 fours, then find the number of dot balls faced by R.
- A.
175
- B.
195
- C.
155
- D.
185
- E.
165
Show answer & explanation
Correct answer: B
Concept
Strike rate links runs and balls by SR = (runs / balls) × 100, so runs = SR × balls / 100 and balls = runs × 100 / SR. In a pie chart a category's share of the total equals its central angle divided by 360°. When a batsman scores only in boundaries, every run comes from a scoring ball (a four or a six), and a dot ball is simply a faced ball that produced no run, so dot balls = total balls faced − scoring balls.
Application
Work each unknown in order, using the Notes:
Q: balls = 180 and SR = 33⅓ = 100/3, so runs(Q) = (100/3) × 180 / 100 = 60.
P (Note III): if P faced 180 balls with his own runs, his SR would be double Q's = 200/3, so runs(P) = (200/3) × 180 / 100 = 120.
P (Note I): SR(P) = 25, so balls(P) = runs(P) × 100 / 25 = 120 × 4 = 480.
R balls (Note IV): balls(R) = balls(P) / 2 = 480 / 2 = 240.
R runs (Note VI): R's run share = 198° / 360° = 55%, so the other two share 45%; total runs = (120 + 60) / 0.45 = 400, hence runs(R) = 55% of 400 = 220.
R's scoring split: 25 fours give 25 × 4 = 100 runs; the remaining 220 − 100 = 120 runs come from sixes, i.e. 120 / 6 = 20 sixes.
Scoring balls of R = 25 fours + 20 sixes = 45 balls.
Dot balls of R = balls(R) − scoring balls = 240 − 45 = 195.
Cross-check
R faced 240 balls scoring 220 runs, giving SR = 220 / 240 × 100 ≈ 91.67, consistent with a boundary-heavy innings. The 45 scoring balls (100 + 120 = 220 runs) together with 195 dot balls account for all 240 deliveries, so the count is internally consistent. The number of dot balls faced by R is 195.