Average
- The average age of the boys in a class is 18 years. The average age of the girls in that class is 12 years. If the ratio of the number of boys and girls in that class is 3 : 2, then the average age of the class is :
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Let the number of boys in the class be 3k and that of girls be 2k.
∴ Average age of class = 3k × 18 + 2k × 12 3k + 2k Average age of class = 54k + 24k 5k
Correct Option: A
Let the number of boys in the class be 3k and that of girls be 2k.
∴ Average age of class = 3k × 18 + 2k × 12 3k + 2k Average age of class = 54k + 24k 5k Average age of class = 78 5k
Average age of class = 15.6 years
- Ram is 20 years younger than Shyam. 5 years ago, the ratio of their ages was 3 : 5. The sum of their present ages is :
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Let Ram’s present age = y years
∴ Shyam’s present age = (y + 20) years
According to the question,5 years ago, y - 5 = 3 y + 20 - 5 5 ⇒ y - 5 = 3 y + 15 5
⇒ 5y – 25 = 3y + 45
⇒ 5y – 3y = 25 + 45
⇒ 2y = 70
⇒ y = 70 ÷ 2 = 35
Correct Option: C
Let Ram’s present age = y years
∴ Shyam’s present age = (y + 20) years
According to the question,5 years ago, y - 5 = 3 y + 20 - 5 5 ⇒ y - 5 = 3 y + 15 5
⇒ 5y – 25 = 3y + 45
⇒ 5y – 3y = 25 + 45
⇒ 2y = 70
⇒ y = 70 ÷ 2 = 35
∴ Sum of present ages of Ram and Shyam = (2y + 20) years
Sum of present ages of Ram and Shyam = (2 × 35 + 20) years = 90 years
- The average age of 5 boys is 12 years. The average age of 3 others is 16 years. The average age of all the 8 boys is :
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Given , The average age of 5 boys = 12 years.
Sum of 5 boys = 12 × 5
The average age of 3 others boys = 16 years.
Sum of 3 others boys = 16 × 3
.Required average = 5 × 12 + 3 × 16 5 + 3 Required average = 60 + 48 8 Required average = 108 8
Correct Option: A
Given , The average age of 5 boys = 12 years.
Sum of 5 boys = 12 × 5
The average age of 3 others boys = 16 years.
Sum of 3 others boys = 16 × 3
.Required average = 5 × 12 + 3 × 16 5 + 3 Required average = 60 + 48 8 Required average = 108 8 Required average = 27 2 Required average = 13 1 years. 2
- There are 30 students in a class. The average age of first 10 students is 12.5 years. The average age of the remaining 20 students is 13.1 years. The average age (in years) of the students of the whole class is
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Here , The average age of first 10 students = 12.5 years
Sum of first 10 students = 12.5 × 10
The average age of the remaining 20 students = 13.1 years.
Sum of remaining 20 students = 13.1 × 20
.Average age = 10 × 12.5 + 20 × 13.1 10 + 20
Correct Option: D
Here , The average age of first 10 students = 12.5 years
Sum of first 10 students = 12.5 × 10
The average age of the remaining 20 students = 13.1 years.
Sum of remaining 20 students = 13.1 × 20
.Average age = 10 × 12.5 + 20 × 13.1 10 + 20
.Average age = 125 + 262 30
Average age = 12.9 years
- The mean weight of 34 students of a school is 42 kg. If the weight of the teacher be included, the mean rises by 400 grams. Find the weight of the teacher (in kg).
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According to question ,
Weight of the teacher = 42 kg. + 35 × 400 kg 1000
Weight of the teacher = 42 + 14 = 56 kg.
Second method to solve this question with the help of given formula :
Here, y = 400 ÷ 100 = 0.4 , n = 34
Correct Option: D
According to question ,
Weight of the teacher = 42 kg. + 35 × 400 kg 1000
Weight of the teacher = 42 + 14 = 56 kg.
Second method to solve this question with the help of given formula :
Here, y = 400 ÷ 100 = 0.4 , n = 34
Weight of teacher = Average + x (n + 1)
Weight of teacher = 42 + 0.4 (34 + 1)
Weight of teacher = 42 + 14 = 56 kg
