Average
- The average of runs of a cricket player of 10 innings was 32. How many runs must he make in his next inning so as to increase his average of runs by 4 ?
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Let the batsman make p runs.
Total runs in 10 innings = 10 × 32 = 320∴ 320 + p = 32 + 4 11
⇒ 320 + p = 36 × 11
⇒ p = 396 – 320 = 76
Second method to solve this question with the help of given formula :
Here, T = 32, N = 11, t = 4
Correct Option: A
Let the batsman make p runs.
Total runs in 10 innings = 10 × 32 = 320∴ 320 + p = 32 + 4 11
⇒ 320 + p = 36 × 11
⇒ p = 396 – 320 = 76
Second method to solve this question with the help of given formula :
Here, T = 32, N = 11, t = 4
Required Run = T + Nt [Here N is taken as (n + 1)]
Required Run = 32 + 11 × 4
Required Run = 32 + 44 = 76
- The average of 9 observations was found to be 35. Later on, it was detected that an observation 81 was misread as 18. The correct average of the observations is :
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Given that , The average of 9 observations = 35
Later on, it was detected that an observation 81 was misread as 18 .
Correct sum of 9 observations = 9 × 35 – 18 + 81
Correct sum of 9 observations = 315 + 63 = 378Correct Option: B
Given that , The average of 9 observations = 35
Later on, it was detected that an observation 81 was misread as 18 .
Correct sum of 9 observations = 9 × 35 – 18 + 81
Correct sum of 9 observations = 315 + 63 = 378
∴ Required correct average = 378 ÷ 9 = 42
- Average weight of 25 persons is increased by 1 kg when one man weighing 60 kg is replaced by a new person. Weight of new person is :
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According to question ,
Total weight increased = 1 × 25 = 25 kg
∴ Weight of new person = weight of man + Total weight increased
Weight of new person = 60 + 25 = 85 kg
Second method to solve this question with the help of given formula :
Here, N = 25, T = 60 , t = 1Correct Option: D
According to question ,
Total weight increased = 1 × 25 = 25 kg
∴ Weight of new person = weight of man + Total weight increased
Weight of new person = 60 + 25 = 85 kg
Second method to solve this question with the help of given formula :
Here, N = 25, T = 60 , t = 1
Weight of New person = T + Nt
Weight of New person = 60 + 25 × 1 = 85 Kg
- The average weight of 12 crewmen in a boat is increased by 1/3 kg, when one of the crewmen whose weight is 55 kg is replaced by a new man. What is the weight of that new man?
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Total increase in weight = 12 × 1 = 4 3
Weight of the new man = Weight of the crewmen + Total increase in weight
∴ Weight of the new man = 55 + 4 = 59 kg
Second method to solve this question with the help of given formula :Here, N = 12, T = 55, t = 1 3
Weight of new man = T + Nt
Correct Option: D
Total increase in weight = 12 × 1 = 4 3
Weight of the new man = Weight of the crewmen + Total increase in weight
∴ Weight of the new man = 55 + 4 = 59 kg
Second method to solve this question with the help of given formula :Here, N = 12, T = 55, t = 1 3
Weight of new man = T + NtWeight of the new man = 55 + 12 × 1 3
Weight of the new man = 55 + 4 = 59 kg.
- A boy found that the average of 20 numbers is 35 when he writes a number ‘61’ instead of ‘16’. The correct average of 20 numbers is
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Given that , The average of 20 numbers = 35
When a boy writes a number ‘61’ instead of ‘16’ , thenCorrect average = 35 + 
61 -16 
20 Correct average = 35 - 45 = 35 - 2.25 = 32.75 20
Second method to solve this question with the help of given formula :
Here, n = 20, m = 35 , a = 16, b = 61
Correct Option: A
Given that , The average of 20 numbers = 35
When a boy writes a number ‘61’ instead of ‘16’ , thenCorrect average = 35 + 61 -16 20 Correct average = 35 - 45 = 35 - 2.25 = 32.75 20
Second method to solve this question with the help of given formula :
Here, n = 20, m = 35 , a = 16, b = 61Correct mean = m + (a - b) n Correct mean = 35 + (16 - 61) 20
Correct mean = 35 - 45 20
Correct mean = 35 – 2.25 = 32.75
