Concept of “Average” [“औसत”]-07

Question: The average age of an adult class is 40 years. 12 new students with an average of 32 years join the class, thereby decreasing the average of the class by 4 years. The original strength of the class was [Ans. (c) 12]

(a) 10    (b) 11    (c) 12    (d) 15   (e) none of these

Solution:

Detailed Explanation:

Concept: Definition: Average: “Average of any set of items is the ‘value’, which is obtained by dividing all the items among them - equally.” In other words, “If all the items of a set is distributed equally among them, then what each will get – that each value is the ‘average’.”   

First Method: Given that the average age of an adult class is 40 years. When 12 new students with an average age of 32 years, join the class, average reduces by 4 years, that is, it becomes 36 years. That means each of 12 students has 4 years less than the 36. That is, 4 × 12 = 48. So, each of the students of adult class should has 48 more in total. But each of the adult student has 4 yrs more. So, 4 into what equals 48? Obviously, it is 12 Ans.

Second Method: The question can also be solved by “Method of Alligation”.  Given that the average age of an adult class is 40 years. When 12 new students with an average age of 32 years, join the class, average reduces by 4 years, that is, it becomes 36 years.

The ratio of students of new students to old adult students = (40-36) : (36-32) = 4:4 = 1:1

No. of students (new) 1 ≡ 12 (given)

So, no. of students (adult class) 1 ≡? 12 (given) Ans.

Third Method: (Usual method): Given that the average age of an adult class is 40 years. When 12 new students with an average age of 32 years, join the class, average reduces by 4 years, that is, it becomes 36 years. Let the no. of students in the adult class is “x” years.

The sum of the ages of 12 new students is (12 ×32) years

The sum of the ages of students of adult class is (x ×40) years

The sum of the ages of 12 new students and adult class together is [(12+x) ×36] years

Now, (12 ×32) + (x ×40) = [(12+x) ×36]

Or, (40 – 36) x = 12 × (40-36)

Or, 4x = 12 × 4

Or, x = 12 Ans.