Average [औसत]-04

Question: In a certain primary school, there are 60 boys of age 12 each, 40 of age 13 each, 50 of age 14 each and 50 of age 15 each. The average age (in years) of the boys of the school is [एक स्कूल में 60 लड़के, प्रत्येक 12 वर्ष के; 40 लड़के, प्रत्येक 13 वर्ष के; 50 लड़के, प्रत्येक 14 वर्ष के और 50 लड़के, प्रत्येक 15 वर्ष के हैं. स्कूल के सभी लड़कों की औसत उम्र (वर्षों में) बताएं.]:  [Ans. (c) 13.45] 

(a) 13.50  (b) 13   (c) 13.45   (d) 14   (e) none of these

Solution: [-60×1+0+50×1+50×2]÷200 = 90÷200 = 0.45                   

Required average = 13+0.45 = 13.45 Ans.

Detailed Explanation:

First Method: Let the assumed mean is 13 (years). For the first group of 60 boys having 12 years each has a shortfall of 60×1= 60 years.

In the second group of 40 boys having 13 years each, there is exactly “0” shortfall or extra.

For the third group of 50 boys having 14 years each, there is excess of 50×1 = 50 years.

For the fourth group of 50 boys having 15 years each, there is excess of 50×2 = 100 years.

Finally, we have -60×1+0+50×1+50×2 = 90 extra which have to be distributed among 200 boys. Each boy will get 0.45 years extra.

Therefore, required average = 13+0.45 = 13.45 Ans.  

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Second Method: The sum of the ages of 60 boys having 12 years each is 60×12 = 720

The sum of the ages of 40 boys having 13 years each is 40×13 = 520

The sum of the ages of 50 boys having 14 years each is 50×14 = 700

The sum of the ages of 50 boys having 15 years each is 50×15 = 750

Now, the sum of the ages of all 200 boys is 720+520+700+750 = 2690

Therefore, their average is 2690/200 = 13.45 years. Ans.