The average height of a certain number of students in a group is 155.6 cm. If 12 students having an average height of 150.5 cm join the group and 7 students having an average height of 159 cm leave the group, the average height of the students in the group will decrease by 34 mm. What is the number of students initially, in the group?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 20
Let the initial number of students is P.
So, the total height of P students = (P × 155.6) cm
Now, total height increased by = (12 × 150.5) = 1806 cm
Then, the total height decreased by = (7 × 159) = 1113 cm
Now, the total change in height = (1806 - 1113) = 693 cm
The final number of stundets = (P + 12 - 7) = (P + 5)
According to the question,
155.6 × P + 693 = (155.6 - 3.4) × (P + 5)
⇒ P = 20