Problem Based on ages
- The average weight of 8 persons of a family is increased by 1 kg when one of the members whose weight is 60 kg is replaced by a new person. The weight of the new person (in kg) is
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Here , n = 8 , Weight of replaced person = 60 kg and increase in Average = 1 kg
Using formula ,
∴ Weight of new person = Weight of replaced person + n × increase in AverageCorrect Option: B
Here , n = 8 , Weight of replaced person = 60 kg and increase in Average = 1 kg
Using formula ,
∴ Weight of new person = Weight of replaced person + n × increase in Average
Weight of new person = 60 + 8 × 1 = 68 kg
- At present a father’s age is 30 years more than that of his only son. What was his age when the son was born?
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Suppose the age of son at present = P years
∴ Present age of the father = Present age of son + 30 years
Present age of the father = P + 30 yearsCorrect Option: B
Suppose the age of son at present = P years
∴ Present age of the father = Present age of son + 30 years
Present age of the father = P + 30 years
Age of father at the birth of his son = Present age of the father - Present age of son = ( P + 30 ) – P = 30 years
- The average age of 19 boys in a class is 21 years. If the teacher’s age is included, the average increases to 22 years. What is the teacher’s age?
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Given that :- The average age of 19 boys in a class = 21 years
Total age of 19 boys = 19 × 21 = 399 years
The average age of 19 boys and teacher = 22 years
Total age of 19 boys and teacher = 20 × 22 = 440 yearsCorrect Option: B
Given that :- The average age of 19 boys in a class = 21 years
Total age of 19 boys = 19 × 21 = 399 years
The average age of 19 boys and teacher = 22 years
Total age of 19 boys and teacher = 20 × 22 = 440 years
∴Teacher’s age = Total age of 19 boys and teacher - Total age of 19 boys
Teacher’s age = 440 – 399 = 41 years
Hence , the age of teacher is 41 years .
- 10 years ago, average age of A and B was 20 years. Average age of A, B and C is 30 years today. How old C will be after 5 years?
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Let the present ages of A, B and C be P years, Q years and R years respectively.
According to question,
Ten years ago, average age of A and B = 20 years.(P - 10) + (Q - 10) = 20 2 Correct Option: C
Let the present ages of A, B and C be P years, Q years and R years respectively.
According to question,
Ten years ago, average age of A and B = 20 years.(P - 10) + (Q - 10) = 20 2
⇒ P – 10 + Q – 10 =40
⇒ P + Q = 60 .....(i)
Average present age of A, B and C = 30 yearsAgain, P + Q + R = 30 3
⇒ P + Q + R = 30 × 3 = 90 ....(ii)
On solving equations (i) and (ii) , we get
R = 30 years
Hence, the age of C after 5 years = 30 + 5 = 35 years
- A father is 3 times as old his son. 8 years ago, the father was 5 times as old as his son. What is the present age of the son?
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Suppose the present age of the son is P years.
Therefore, the present age of father will be 3P years.
According to question , Eight years ago, 5 × ( the present age of the son - 8 years ) = ( the present age of father - 8 years )
5(P – 8) = 3P – 8
⇒ 5P – 40 = 3P – 8
⇒ 5P – 3P = 40 – 8
⇒ 2P = 32Correct Option: C
Suppose the present age of the son is P years.
Therefore, the present age of father will be 3P years.
According to question , Eight years ago, 5 × ( the present age of the son - 8 years ) = ( the present age of father - 8 years )
5(P – 8) = 3P – 8
⇒ 5P – 40 = 3P – 8
⇒ 5P – 3P = 40 – 8
⇒ 2P = 32∴ P = 32 = 16 years 2
Therefore , the present age of the son is 16 years.