Question: The
average age of 34 boys in a class is 28.5 years. If the teacher’s age is
included, the average age of the boys and the teacher becomes 29 years. What is
the teachers’ age? [किसी कक्षा के 34 छात्रों की औसत आयु 28.5 वर्ष है. यदि शिक्षक की आयु भी
शामिल कर ली जाये, तो शिक्षक सहित छात्रों की औसत आयु 29 वर्ष हो जाती है. शिक्षक
की आयु क्या है? ] Ans. (c) 46
year
(a) 45 year (b) 46.5 year
(c) 46 year (d) 45.5
years (e) none of these
Detailed solution:
First Method:
Since the average age of students including teacher is 29 yrs, so the teacher should
have 29 yrs at least. Also, to increase the age of the students from 28.5 to 29
yrs, that is, to increase the age of each of the 34 students by 0.5 yrs; he must
have 17 yrs. So, the age of the teacher = 29 yrs + 17 yrs = 46 yrs Ans.
Second Method: Age
of the teacher = average age of students including teacher + difference between
the averages × no.
of students = 29 yrs + (29 – 28.5) × 34 yrs
= 29 yrs + 0.5 × 34 = 29
yrs + 17 yrs = 46 yrs Ans.
Third Method: Age
of the teacher = average age of students + difference between the averages × total no. of students including teacher
= 28.5 yrs + (29 – 28.5) × 35 yrs
= 28.5 yrs + 0.5 × 35 = 28.5
yrs + 17.5 yrs = 46 yrs Ans.
Fourth Method: Age
of teacher = total age of students including teacher – total age of students = [29
× 35 – 28.5 × 34] yrs = [1015 – 969]
yrs = 46 yrs Ans. (Since sum = average × no.) (usual method)
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