In a class with a certain number of students if one student weighing 50 kg is added then the average weight of the class increases by 1 kg. If one more student weighing 50 kg is added then the average weight of the class increases by 1.5 kg over the original average. What is the original average weight (in kg) of the class?a)46b)4c)2d)47Correct answer is option 'D'. Can you explain this answer?

Question

Answer

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.

Answer

Given Information:
- Addition of one student weighing 50 kg increases the average weight of the class by 1 kg.
- Addition of one more student weighing 50 kg increases the average weight of the class by 1.5 kg over the original average.

Solution:

Let the original number of students in the class be 'n' and the original average weight of the class be 'x' kg.

When one student weighing 50 kg is added:
- Total weight of the class = (n*x) + 50
- Total number of students in the class = n + 1
- New average weight of the class = ((n*x) + 50) / (n + 1)
- Given that the average weight increases by 1 kg:
(x + 1) = (((n*x) + 50) / (n + 1))

When one more student weighing 50 kg is added:
- Total weight of the class = ((n+1)*(x+1)) + 50
- Total number of students in the class = n + 2
- New average weight of the class = (((n+1)*(x+1)) + 50) / (n + 2)
- Given that the average weight increases by 1.5 kg over the original average:
(x + 1.5) = ((((n+1)*(x+1)) + 50) / (n + 2))

Solving the above two equations simultaneously, we get:
x = 47

Therefore, the original average weight of the class was 47 kg. Option D is correct.

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