In a class with a certain number of students if one student weighing 5...
Let x be the original average and n be the number of students. Let x1, x2, x3 ,. . . .. xn be the weights of n students respectively. Therefore,
Solving (1) and (2), we get
x + n = 49..... (4)
Solving (1) and (3), we get
4x + 3n = 194 ...... (5)
Now, Solving (4) and (5), we get
n = 2, x = 47
So, the original average weight (in kg) of the class = 47
Alternate Solution :
Let x be the original average and n be the number of students.
From the first increase in the average,
we get 50 - x = n + 1
From the second increase in the average,
we get 100 - 2x = 1.5 (n + 2)
Solving, we get the value of x = 47.