Practice Questions
Concept Explanation
Age problems use the same average formulas. Remember: after t years, every person's age increases by t, so the average also increases by t.
Key Rules
- Average age = Total of ages / Number of persons
- After t years, new average = Old average + t
- When a person joins or leaves, apply addition/removal formulas.
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Q1 EasyThe average age of 36 students of a class is 14 years. When the age of the teacher is included, the average becomes 15 years. The age of the teacher is:ExplanationSum of ages of 36 students = 36 × 14 = 504 years. Sum including teacher = 37 × 15 = 555 years. Teacher's age = 555 − 504 = 51 years.
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Q2 Easy9 persons meet for a party. The average age of 8 of them is 25 years. When the 9th person joins, the average age of all 9 becomes 26 years. The age of the 9th person is:ExplanationSum of ages of 8 persons = 8 × 25 = 200 years. Sum of ages of 9 persons = 9 × 26 = 234 years. Age of the 9th person = 234 − 200 = 34 years.
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Q3 EasyThe average age of 30 students of a class is 9 years. If the age of their teacher is included, the average age becomes 10 years. The age of the teacher is:ExplanationSum of students' ages = 30 × 9 = 270. Sum including teacher = 31 × 10 = 310. Teacher's age = 310 − 270 = 40 years.
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Q4 EasyTwo years ago, the average age of 5 friends was 20 years. Their present average age is:ExplanationAfter t years, average age also increases by t. Present average = 20 + 2 = 22 years.
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Q5 EasyThe average age of a family of 4 members is 25 years. A newborn baby joins the family. The new average age is:ExplanationPresent sum of 4 members = 4 × 25 = 100. With a newborn (age 0), new average = 100 / 5 = 20 years.
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Q6 EasyThe average age of father and son is 30 years. If the father is 44 years old, the son's age is:ExplanationSum of ages = 2 × 30 = 60. Son's age = 60 − 44 = 16 years.
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Q7 EasyPresent average age of 4 members is 28 years. After 5 years, their average age will be:ExplanationEach member gains 5 years, so the average also increases by 5. Future average = 28 + 5 = 33 years.
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Q8 EasyThe sum of ages of A and B is 48 years and their average is 24 years. After 6 years, their average age will be:ExplanationPresent average is 24 years (consistent with sum 48). After 6 years average increases by 6, so new average = 24 + 6 = 30 years.
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Q9 MediumThe average age of a husband and his wife was 23 years at the time of their marriage. After five years they have a one-year old child. The average age of the family at present is:ExplanationAt marriage, sum of ages of husband and wife = 2 × 23 = 46 years. After 5 years their combined age = 46 + 10 = 56 years. With the 1-year-old child, present family sum = 56 + 1 = 57 years. Present average = 57 / 3 = 19 years.
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Q10 MediumAverage age of 6 persons is 24 years. A person aged 38 years joins them. The new average age is:ExplanationOld sum = 6 × 24 = 144. New sum = 144 + 38 = 182. New average = 182 / 7 = 26 years.
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Q11 MediumAverage age of 8 persons is 25 years. One person aged 32 years leaves. The new average age is:ExplanationOld sum = 8 × 25 = 200. New sum = 200 − 32 = 168. New average = 168 / 7 = 24 years.
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Q12 MediumAverage age of 5 members is 40 years. A person aged 50 years joins. The new average age is:ExplanationOld sum = 5 × 40 = 200. New sum = 200 + 50 = 250. New average = 250 / 6 = 125/3 ≈ 41.67 years.
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Q13 HardThe average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is:Explanation3 years ago, sum of H + W + C = 3 × 27 = 81, so present sum = 81 + 9 = 90. 5 years ago, W + C = 2 × 20 = 40, so present W + C = 40 + 10 = 50. Present age of husband = 90 − 50 = 40 years.
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Q14 HardThree years ago, the average age of a family of 5 members was 17 years. A baby having been born in the meantime, the average age of the family is the same today as it was three years ago. The present age of the baby is:Explanation3 years ago, sum of 5 members = 5 × 17 = 85. Today those 5 members total 85 + 15 = 100. Today the family of 6 still averages 17, so present sum = 6 × 17 = 102. Baby's present age = 102 − 100 = 2 years.
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DS1 Easy
In a family-age practice set, what is the average age of the three persons?
Statement IThe ages of the three persons are 18, 22 and 20 years.
Statement IIThe sum of their ages is 60 years.
ExplanationStatement I: average = (18 + 22 + 20) / 3 = 20. Statement II: average = 60 / 3 = 20. Each statement alone is sufficient. -
DS2 Easy
During an aptitude drill, what will the average age of the group be after 5 years?
Statement IThe present average age of the group is 28 years.
Statement IIThere are 4 members in the group.
ExplanationAfter t years the average rises by t regardless of group size. Statement I alone: future average = 28 + 5 = 33 years. Statement II alone is insufficient.
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DS3 Medium
A placement question asks for the son's present age. What is the son's age?
Statement IThe average age of father and son is 30 years.
Statement IIThe father is 44 years old.
ExplanationStatement I gives total = 60 but not individual ages. Statement II alone lacks the son's age. Together: son = 60 − 44 = 16 years. -
DS4 Medium
A campus DS set asks for the new average age after one person joins. What is the new average?
Statement IThe average age of 6 persons is 24 years.
Statement IIThe person who joins is 38 years old.
ExplanationTogether: new average = (144 + 38) / 7 = 182 / 7 = 26 years. Each statement alone is insufficient.