Question: Among 100 students, the average marks in English is 78. If the 60 girls scored an average of 84, determine the average score of the remaining boys.

Solution:

ধরি,

ছাত্রদের গড় নম্বর = x 

100 জন শিক্ষার্থীর মোট নম্বর = 100 × 78 = 7800 

এবং 60 জন ছাত্রীর মোট নম্বর = 60 × 84 = 5040

প্রশ্নমতে,

5040 + (100 - 60)x = 7800

⇒ 5040 + 40x = 7800

⇒ 40x= 7800 - 5040

⇒ 40x = 2760

⇒ ক = 2760/40 

⇒ ক = 69

∴ 40 জন ছাত্রের গড় নম্বর = 69

Question: Average age of 15 students of a class is 15 years. Out of these the average age of 5 students is 14 years and that of the other 9 students is 16 years. The age of the 15th student is-

Solution:
Given that
Average age of 15 students = 15 years
Average age of 5 students = 14 years
Average age of 9 students = 16 years

Now,
Total age of all 15 students = 15 × 15 = 225 years
Total age of 5 students = 5 × 14 = 70 years
Total age of 9 students = 9 × 16 = 144 years 

∴ Age of the 15th student = 225 - (70 + 144) = 225 - 214 = 11 years