Average
- The average age of 45 persons is decreased by 1/9 year when one of them of 60 years is replaced by a new comer. Then the age of the new comer is :
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Here , Age of replaced person = 60 years
According to question ,Reduction in total age of 45 persons = 45 × 1 9 Age of the new person = 60 - 45 × 1 = 55 years 9
Second method to solve this question with the help of given formula :Here , X = 45 , n = 1 9
Correct Option: B
Here , Age of replaced person = 60 years
According to question ,Reduction in total age of 45 persons = 45 × 1 9 Age of the new person = 60 - 45 × 1 = 55 years 9
Second method to solve this question with the help of given formula :Here , X = 45 , n = 1 9 Age of new comer = Age of replaced member – Xn = 60 – 45 × 1 9
Age of new comer = 60 – 5 = 55 years
- 3 years ago, the average age of a family of 5 members was 17 years. A baby having been born, the average age of the family is the same today. The present age of the baby is :
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Given that , 3 years ago, the average age of a family of 5 members = 17 years
Total age of 5 members, 3 years ago = 17 × 5 = 85 years
Total present age of 5 members = (85 + 3 × 5) = 100 years
Born on a new baby , the average age of the family of 6 members = 17 years
Total present age of 6 members = 17 × 6 = 102 years
∴ Age of the baby = 102 – 100 = 2 years
Second method to solve this question with the help of given formula :
∴ Here, t = 3, N = 5 , T = 17, n = 1Correct Option: B
Given that , 3 years ago, the average age of a family of 5 members = 17 years
Total age of 5 members, 3 years ago = 17 × 5 = 85 years
Total present age of 5 members = (85 + 3 × 5) = 100 years
Born on a new baby , the average age of the family of 6 members = 17 years
Total present age of 6 members = 17 × 6 = 102 years
∴ Age of the baby = 102 – 100 = 2 years
Second method to solve this question with the help of given formula :
∴ Here, t = 3, N = 5 , T = 17, n = 1
Present age of baby = nT – Nt
Present age of baby = 1 × 17 – 5 × 3 = 17 – 15 = 2 years
- Out of 10 teachers of a school, one teacher retires and in his place, a new teacher of age 25 years joins. As a result, average age of teachers reduces by 3 years. The age of the retired teacher is
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Here, Age of new teacher = 25 years
Total age decreased = 10 × 3 = 30 years.
∴ Age of the retired teacher = Age of new teacher + Total age decreased
Age of the retired teacher = 25 + 30 = 55 years.
Second method to solve this question with the help of given formula :
Here, n = 10, X = 3
Age of new teacher = Age of retired teacher – XnCorrect Option: B
Here, Age of new teacher = 25 years
Total age decreased = 10 × 3 = 30 years.
∴ Age of the retired teacher = Age of new teacher + Total age decreased
Age of the retired teacher = 25 + 30 = 55 years.
Second method to solve this question with the help of given formula :
Here, n = 10, X = 3
Age of new teacher = Age of retired teacher – Xn
25 = Age of retired teacher – 10 × 3
⇒ Age of retired teacher = 25 + 30 = 55 years
- Average age of 6 sons of a family is 8 years. Average age of sons together with their parents is 22 years. If the father is older than the mother by 8 years, the age of mother (in years) is :
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Let the mother’s age = y years
∴ Father’s age = (y + 8) years
Sum of age of 6 sons = 8 × 6 = 48 years
Sum of age of 6 sons and parents = 22 × 8 = 176 years.
∴ Age of Parents = 176 – 48 = 128 years
⇒ y + y + 8 = 128
⇒ 2y = 120Correct Option: C
Let the mother’s age = y years
∴ Father’s age = (y + 8) years
Sum of age of 6 sons = 8 × 6 = 48 years
Sum of age of 6 sons and parents = 22 × 8 = 176 years.
∴ Age of Parents = 176 – 48 = 128 years
⇒ y + y + 8 = 128
⇒ 2y = 120
⇒ y = 60
Hence, mother’s age = 60 years
- The average age of 30 boys in a class is 15 years. One boy, aged 20 years, left the class, but two new boys came in his place whose age differ by 5 years. If the average age of all the boys now in the class becomes 15 years, the age of the younger newcomeris :
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According to question ,
Total age of 30 boys = 30 × 15 = 450 years
One boy, aged 20 years, left the class
Now, total age of 29 boys = 450 – 20 = 430 years
Again, two new boys join the class
Then, the total age of 31 boys = 15 × 31 = 465 years
∴ Age of two new boys = 465 – 430 = 35 years
Let the individual age of two boys be p and q years
∴ p + q = 35
According to the question ,
⇒ p – q = 5
∴ 2p = 40
p = 40 ÷ 2 = 20 yearsCorrect Option: B
According to question ,
Total age of 30 boys = 30 × 15 = 450 years
One boy, aged 20 years, left the class
Now, total age of 29 boys = 450 – 20 = 430 years
Again, two new boys join the class
Then, the total age of 31 boys = 15 × 31 = 465 years
∴ Age of two new boys = 465 – 430 = 35 years
Let the individual age of two boys be p and q years
∴ p + q = 35
According to the question ,
⇒ p – q = 5
∴ 2p = 40
p = 40 ÷ 2 = 20 years
∴ q = 15 years
∴ Age of the younger new comer = 15 years
