model 9 average on cricket/exam Section-Wise Topic Notes With Detailed Explanation And Example Questions

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Questions : The averages of runs scored by a cricket player in 11 innings is 63 and the average of his first six innings is 60 and the average of last six innings is 65. Find the runs scored by him in the sixth innings.

(a) 54

(b) 57

(c) 60

(d) 67

The correct answers to the above question in:

Answer: (b)

Runs scored by the cricketer in the 6th innings

= 6 × 60 + 6 × 65 – 11 × 63

= 360 + 390 – 693 = 57

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Question : 1

A batsman in his 12th innings makes a score of 63 runs and there by increases his average scores by 2. What is his average after the 12th innings?

a) 39

b) 87

c) 13

d) 49

Answer: (a)

Extra runs = 12 × 2 = 24

∴ Required average = 63 – 24 = 39

Question : 2

A cricketer had a certain average of runs for his 64 innings. In his 65th innings, he is bowled out for no score on his part. This brings down his average by 2 runs. His new average of runs is

a) 128

b) 68

c) 130

d) 70

Answer: (a)

Let the cricketer’s average of runs for his 64 innings be x runs.

∴ Total number of runs in 64 innings = 64x

According to the question,

${64x+0}/65$ = x-2

⇒ 64x = 65x – 130

⇒ x = 130

∴ New average of runs = x – 2

= 130– 2 = 128

Question : 3

The average of runs scored by a cricketer in his 99 innings is 99. How many runs will he have to score in his 100th innings so that his average of runs in 100 innings may be 100?

a) 99

b) 101

c) 100

d) 199

Answer: (d)

Number of runs scored in 100th innings

= 100 × 100 – 99 × 99

= 10000 – 9801 = 199

OR

Increase in average = 1 run

∴ Runs scored in 100th innings = 100 + 99 = 199

Question : 4

A cricketer whose bowling average is 12.4 runs per wicket, takes 5 wickets for 26 runs and thereby decreases his average by 0.4. The number of wickets taken by him till the last match was

a) 72

b) 85

c) 64

d) 80

Answer: (b)

Required number of wickets = x (let)

According to question,

12.4 × x + 26 = (x + 5) (12.4 – 0.4) = (x + 5) × 12

⇒ 12.4x + 26 = 12x + 60

⇒ 12.4x – 12x = 60 – 26

⇒ 0.4x = 34

⇒ x = $34/{0.4}$ = $340/4$ = 85

Question : 5

A batsman makes a score of 87 runs in the 17th innings and thus increased his average by 3. Find his average after 17th innings.

a) 87

b) 84

c) 39

d) 90

Answer: (c)

Average runs in 16 innings = 87 – 17 × 3 = 87 – 51 = 36

∴ Required average = 36 + 3 = 39 runs

Question : 6

A cricketer has a certain average of runs for his 8 innings. In the ninth innings, he scores 100 runs, thereby increases his average by 9 runs. His new average of runs is

a) 24

b) 32

c) 20

d) 28

Answer: (d)

Let the average of runs of the cricketer in 8 innings be x .

According to the question,

${8x+100}/9$=x+9

⇒ 8x + 100 = 9x + 81

⇒ x = 100 – 81 = 19

∴ New average of runs = 19 + 9 = 28

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