The average age of a certain number of students in a college club is 20 years. Later, 27 new students, whose average age is 22 years, joined the club. 12 students, whose average age is 19 years, left the club. As a result of this change, the average age of all the students increases by 2 years. What is the present number of students in the club?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 33.
We know that,
Average = Sum of observations/Number of observations
Let the number of students initially be x
According to the question;
⇒ x × 20 + (27 × 22) - (12 × 19) = (x + 27 - 12) × 22
⇒ 20x + 594 - 228 = (x + 15) × 22
⇒ 20x + 366 = 22x + 330
⇒ 2x = 36
⇒ x = 18
Hence, the present number of students in the club = x + 27 - 12
⇒ 18 + 27 - 12 = 33