In a cricket match, a team made a score of 256 runs which included 16 fours and 7 sixes. From the remaining runs, 20% were scored by taking three runs in a ball, 44% by taking two runs in a ball and the remaining were taken as single runs per ball. If the team played a total of 300 balls, on what percentage of the balls no runs were scored?

In a cricket match, a team made a score of 256 runs which included 16 fours and 7 sixes. From the remaining runs, 20% were scored by taking three runs in a ball, 44% by taking two runs in a ball and the remaining were taken as single runs per ball. If the team played a total of 300 balls, on what percentage of the balls no runs were scored? Correct Answer 60%

No. of runs scored by running between wickets = 256 – (4 × 16) – (6 × 7) = 256 – 64 – 42 = 150

⇒ No. of runs scored by taking three runs per ball = 20% of 150 = 30

⇒ No. of balls on which three runs were scored = 30/3 = 10

Also,

No. of runs scored by taking two runs per ball = 44% of 150 = 66

⇒ No. of balls on which two runs were scored = 66/2 = 33

⇒ No. of balls on which singe runs were scored = No. of single runs scored = 150 – 30 – 66 = 54

∵ 16 fours and 7 sixes were scored on one ball each

⇒ Total no. of balls on which runs were scored = 10 + 33 + 54 + 16 + 7 = 120

⇒ No. of balls on which no runs were scored = 300 – 120 = 180

∴ Percentage of balls on which no runs were scored = 180/300 × 100 = 60%