In Mahesh’s opinion, his age is greater than 56 years but less than 63 years.…
2025
In Mahesh’s opinion, his age is greater than 56 years but less than 63 years. His sister thinks that his age cannot be greater than 59 years and his mother’s view his age is greater than 51 years but less than 60 years. What is his average age?
- A.
60 years
- B.
54 years
- C.
58 years
- D.
59 years
Attempted by 8 students.
Show answer & explanation
Correct answer: C
Concept: When several people give overlapping range estimates for an unknown quantity, the values consistent with every estimate are exactly the intersection of all the stated inequality ranges. If that intersection contains more than one integer and the question asks for the 'average', the required value is the arithmetic mean of every integer in that intersection.
Application
Let Mahesh's age be x. Write each opinion as an inequality — Mahesh's own: 56 < x < 63; his sister's: x ≤ 59; his mother's: 51 < x < 60.
Intersect the three ranges. The strictest lower bound is x > 56 (Mahesh's, tighter than the mother's x > 51). The strictest upper bound is x ≤ 59 (the sister's, tighter than both x < 63 and x < 60).
So the combined range is 56 < x ≤ 59. The integers satisfying this are 57, 58 and 59.
Average = (57 + 58 + 59) / 3 = 174 / 3 = 58.
Cross-check: 56 is excluded because it is not strictly greater than 56, and 60 is excluded because it fails both the sister's 'not greater than 59' limit and the mother's 'less than 60' limit — confirming exactly three qualifying ages.
Answer: The average age is 58 years.