In a class there are certain number of students and their average weight is 15 kg. If 6 students wit

M4maths Previous Puzzles

24 May 2022 Average

In a class there are certain number of students and their average weight is 15 kg. If 6 students with average weight of 18 kg join or 9 students with average weight of 14 kg leaves, then in both the cases average weight of students remains same. How many students are there initially in a class ?

OPtion

1) 48
2) 36
3) 42
4) 39
5) 24
6) 30
7) 33
8) 21
9) 27
10) None of these

Solution

Initially if there are 'x' students in a class, then their total weight = 15x kg.
When 6 students of average weight 18 kg joins, then average of all students = (15x + 18*6) / (x+6) Kg
When 9 students of average weight 14 kg leaves, then average of all students = (15x - 14*9) / (x-9) Kg
As both cases,the averages are same .'. (15x + 18*6) / (x+6) = (15x - 14*9) / (x-9)
(5x + 36) / (x+6) = (5x - 42) / (x-9)
5x² - 45x + 36x - 324 = 5x² - 42x + 30x - 252
3x = 72
x = 24
Hence, there are 24 students initially in a class.

Correct Option: 5 Best Solution (2)

G.S.Kantharao   1 year AGO

Let x is the number of students. Then
(15x+108)/(x+6)=(15x-126)/(x-9)
(15x+108)(x-9)=(15x-126)(x+6)
15x^2+108x-135x-972=
15x^2-126x+90x-756
=>9x=216
=>x=24
My option is 5👈

Like? Yes (5) | No   

RAMADURAI NATESAN   1 year AGO

Let n be initial no.of students.
(15n + 108 ) /(n+6) = (15n-126)/(n - 9).
Solving , n = 24

Like? Yes | No (1)