In a test, the average marks scored by 20 students of a class is 43 and those by the remaining students is 47.5. If the average marks scored by all the students of the class is 45, then how many students are there in the class?
Answer & explanation
Correct answer: option 3
Average = \(\frac{Sum\; of \;all\; observation }{ Total \; number\; of \;observation }\)
Sum of marks of 20 students = 20 × 43 = 860
Sum of marks of remaining students i.e.x = x × 47.5 = 47.5x
Total marks of all students = 45 × ( x + 20 )
⇒ 45 × ( x + 20 ) = 860 + 47.5x
⇒ 2.5x = 900 - 860
⇒ 2.5x = 40
x = 16
Total students in class = 20 + 16 = 36
The correct answer is Option (3) → 36