Average
- If the average marks of three batches of 55, 60 and 45 students respectively is 50, 55 and 60, then the average marks of all the students is
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We find the required average with the help of given formula ,
Here, n1 = 55 , a1 = 50
n2 = 60 , a2 = 55 , n3 = 45 , a3 = 60∴ Average = n1 + n2 + n3 The required average marks = 55 × 50 + 60 × 55 + 45 × 60 55 + 60 + 45
Correct Option: A
We find the required average with the help of given formula ,
Here, n1 = 55 , a1 = 50
n2 = 60 , a2 = 55 , n3 = 45 , a3 = 60∴ Average = n1 + n2 + n3 The required average marks = 55 × 50 + 60 × 55 + 45 × 60 55 + 60 + 45 The required average marks = 2750 + 3300 + 2700 160 The required average marks = 8750 = 54.68 160
- The average of the marks obtained in an examination by 8 students was 51 and by 9 other students was 68. The average marks of all 17 students was :
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The average of the marks obtained in an examination by 8 students = 51
Sum of total number of 8 students in exam = 8 × 51 = 408
The average of the marks obtained in an examination by 9 other students = 51
Sum of total number of 9 students in exam = 9 × 68 = 612∴ Required average = 408 + 612 17 Required average = 1020 = 60 17
Second method to find the required average ,
Here, n1 = 8, a1 = 51
n2 = 9, a2 = 68∴ Average = n1 + n2
Correct Option: C
The average of the marks obtained in an examination by 8 students = 51
Sum of total number of 8 students in exam = 8 × 51 = 408
The average of the marks obtained in an examination by 9 other students = 51
Sum of total number of 9 students in exam = 9 × 68 = 612∴ Required average = 408 + 612 17 Required average = 1020 = 60 17
Second method to find the required average ,
Here, n1 = 8, a1 = 51
n2 = 9, a2 = 68∴ Average = n1a1 + n2a2 n1 + n2 Average = 8 × 51 + 9 × 68 8 + 9 Average = 408 + 612 17 Average = 1020 = 60 marks. 17
- The average age of 11 players of a cricket team is increased by 2 months when two of them aged 18 years and 20 years are replaced by two new players. The average age of the new players is
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On the basis of given details in question ,
Total increase = 11 × 2 = 22 months
∴ Sum of the age of both cricketers = (18 + 20) years 22 months
Sum of the age of both cricketers = 38 years 22 monthsCorrect Option: C
On the basis of given details in question ,
Total increase = 11 × 2 = 22 months
∴ Sum of the age of both cricketers = (18 + 20) years 22 months
Sum of the age of both cricketers = 38 years 22 months∴ Average age = 38 years 22 months = 19 years 11 months 2
- The average score of a-class of boys and girls in an examination is A. The ratio of boys and girls in the class is 3 : 1. If the average score of the boys is A + 1, the average score of the girls is
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Let the number of boys in the class be 3k. The ratio of boys and girls in the class is 3 : 1, then the number of girls in the class is k.
∴ Average score of the girls = (3k + k) × A - 3k(A + 1) k Average score of the girls = 4kA - 3kA -3k k
Correct Option: D
Let the number of boys in the class be 3k. The ratio of boys and girls in the class is 3 : 1, then the number of girls in the class is k.
∴ Average score of the girls = (3k + k) × A - 3k(A + 1) k Average score of the girls = 4kA - 3kA -3k k Average score of the girls = kA - 3k = k(A - 3) = A - 3 k k
- The average monthly salary of the workers in a workshop is Rs. 8,500. If the average monthly salary of 7 technicians is Rs. 10,000 and average monthly salary of the rest is Rs. 7,800, the total number of workers in the workshop is
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Let the number of workers be n.
According to the question,
7 × 10000 + (n – 7) 7800 = n × 8500
⇒ 700 + 78x – 78 × 7 = 85n
⇒ 85n – 78n = 700 – 546Correct Option: C
Let the number of workers be n.
According to the question,
7 × 10000 + (n – 7) 7800 = n × 8500
⇒ 700 + 78x – 78 × 7 = 85n
⇒ 85n – 78n = 700 – 546
⇒ 7n = 154
⇒ n = 154 ÷ 7 = 22
