Average
- In a family of 8 adults and some minors, the average consumption of rice per head per month is 10.8 kg; while the average consumption for adults is 15 kg per head and for minors it is 6 kg per head. The number of minors in the family is :
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Let the number of minors be y.
According to the question,8 × 15 + y × 6 = 10.8 8 + y
⇒ 120 + 6y = 86.4 + 10.8y
⇒ 10.8y – 6y = 120 – 86.4
Correct Option: C
Let the number of minors be y.
According to the question,8 × 15 + y × 6 = 10.8 8 + y
⇒ 120 + 6y = 86.4 + 10.8y
⇒ 10.8y – 6y = 120 – 86.4
⇒ 4.8y = 33.6
⇒ y = 336 ÷ 48 = 7
- The average age of 15 students of a class is 15 years. Out of these the average age of 5 students is 14 years and that of the other 9 students is 16 years. The age of the 15th student is
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Given that , The average age of 15 students = 15 years.
Total age of 15 students = 15 × 15 = 225 years.
The average age of 5 students = 14 years.
Total age of 5 students = 5 × 14 = 70 years
The average age of 9 students = 16 years.
Total age of other 9 students = 9 × 16 = 144 yearsCorrect Option: A
Given that , The average age of 15 students = 15 years.
Total age of 15 students = 15 × 15 = 225 years.
The average age of 5 students = 14 years.
Total age of 5 students = 5 × 14 = 70 years
The average age of 9 students = 16 years.
Total age of other 9 students = 9 × 16 = 144 years
∴ The age of 15th student = 225 – (70 + 144) = 225 – 214 = 11 years.
- The average salary of all the workers in a workshop is ₹8000. The average salary of 7 technicians is ₹12000 and the average salary of the rest is ₹6000. The total number of workers in the workshop is
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Let the total number of workers be n.
Total salary of all the workers = 8000n
Total salary of 7 technicians = 7 × 12000 = ₹84000
Total salary of (n – 7) workers = (n – 7) 6000
∴ (n – 7) 6000 + 84000 = 8000 n
⇒ 8000n – 6000n = 84000 – 42000Correct Option: B
Let the total number of workers be n.
Total salary of all the workers = 8000n
Total salary of 7 technicians = 7 × 12000 = ₹84000
Total salary of (n – 7) workers = (n – 7) 6000
∴ (n – 7) 6000 + 84000 = 8000 n
⇒ 8000n – 6000n = 84000 – 42000
⇒ 2000n = 42000
⇒ n = 42000 ÷ 2000 = 21
- The average of marks obtained by 120 candidates in a certain examination is 35. If the average marks obtained by passed candidates are 39 and those of the failed candidates are 15, what is the number of candidates who passed the examination ?
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The average of marks obtained by 120 candidates = 35.
Let the number of successful students = y
∴ Number of unsuccessful students = 120 – y
According to the question,
⇒ y × 39 + (120 – y) × 15 = 120 × 35
⇒ 39y – 15y + 1800 = 4200Correct Option: A
The average of marks obtained by 120 candidates = 35.
Let the number of successful students = y
∴ Number of unsuccessful students = 120 – y
According to the question,
⇒ y × 39 + (120 – y) × 15 = 120 × 35
⇒ 39y – 15y + 1800 = 4200
⇒ 24y = 4200 – 1800 = 2400
⇒ y = 100
- The arithmetic mean of the scores of a group of students in a test was 52. The brightest 20% of them secured a mean score of 80 and the dullest 25% a mean score of 31.The mean score of remaining 55% is :
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Given , The arithmetic mean of the scores of a group of students in a test = 52.
Let mean score of remaining 55% = y
According to question ,52 = 20 × 80 + 25 × 31 + 55 × y 100
⇒ 5200 = 1600 + 775 + 55y
⇒ 55y = 5200 –1600 – 775
Correct Option: C
Given , The arithmetic mean of the scores of a group of students in a test = 52.
Let mean score of remaining 55% = y
According to question ,52 = 20 × 80 + 25 × 31 + 55 × y 100
⇒ 5200 = 1600 + 775 + 55y
⇒ 55y = 5200 –1600 – 775
⇒ 55y = 2825
∴ y = 2825 ÷ 55 = 51.36 ≈ 51.4%
