Question

The average score of a batsman in 40 innings is 80. He played 10 more innings. If 72 is the score in his 50 innings. Which of the given statements is/are correct?

I. Average score in next 10 innings is more than 72.

II. Average score in next 10 innings is same as the number of innings initially.

III. Total score of next 10 innings is a 3-digit number divisible by 16.

1. Only I is correct
2. I and II are correct
3. I and III are correct
4. II and III are correct

Answer 1

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