Correct Answer - Option 4 : II and III are correct
Given:
Average score in 40 innings = 80
Average score in 50 innings = 72
Formula Used:
Average = Sum of values/Number of values
Calculation:
Sum of score in 40 innings/40 = 80
⇒ Sum of score in 40 innings = 3200
Sum of score in 50 innings/50 = 72
⇒ Sum of score in 50 innings = 3600
⇒ 3200 + Sum of score in 10 innings = 3600
⇒ Sum of score in 10 innings = 400
Average score in 10 innings = 400/10
⇒ 40
I. Average score in next 10 innings is more than 72
40 < 70
⇒ I is not true.
II. Average score in next 10 innings is same as the number of innings initially.
Average score in next 10 innings = 40
Number of innings initially = 40
⇒ II is correct.
III. Total score of next 10 innings is a 3 digit number divisible by 16.
Total score of next 10 innings = 400
400 is a three-digit number divisible by 16.
⇒ III is correct.
∴ II and III are correct.
Short Trick:
Innings 40 10 50
Score 80 72
(+ 8) × 40 = + 320 – 320/10 = – 32
Average of 10 innings = 72 – 32 = 40