Question: The batting average for 27 innings of a cricket player is 47 runs. His highest score in an innings exceeds his lowest score by 157 runs. If these two innings are excluded, the average score of the remaining 25 innings is 42 runs. Find his highest score in an innings.

Solution:
Given that,
The batting average for 27 innings of a cricket player is 47 runs.
His highest score exceeds his lowest score by 157 runs.
If these two innings are excluded, the average of the remaining 25 innings is 42 runs.

Now,
Sum of runs for 27 innings of a cricket player = 47 × 27 = 1269
Sum of runs for 25 innings of a cricket player = 42 × 25 = 1050

∴ Sum of remaining 2 innings = 1269 - 1050 = 219

Let,
The minimum score be x and the maximum score be x + 157

According to the question,
x + x + 157 = 219
⇒ 2x = 219 - 157
⇒ 2x = 62
∴ x = 31

So, highest score = 157 + 31 = 188

সমাধানঃ
আমরা জানি,
n সংখ্যক সংখ্যার গুণোত্তর গড় বা জ্যামিতিক গড় 
∴ 2, 8 এবং 32 এর জ্যামিতিক গড় = (2 × 8 × 32)1/3
= (512)1/3
= (83)1/3
= 8

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