Question

The average weight of the students in a group was 75.4 kg. Later on, four students having weights 72.9 kg, 73.8 kg, 78.5 kg and 88.4 kg respectively, joined the group. As a result, the average weight of all the students in the group increased by 0.24 kg. What was the number of students in the group initially?

1. 46
2. 48
3. 50
4. 51

Answer 1

Correct Answer - Option 1 : 46

Given:

The average weight of the students in a group was 75.4 kg. Later on, four students having weights 72.9 kg, 73.8 kg, 78.5 kg and 88.4 kg respectively, joined the group. As a result, the average weight of all the students in the group increased by 0.24 kg.

Concept used:

Average

Calculation:

Let us suppose that the total number of students are x.

So by using the formula for average:

\(\dfrac{{{\rm{Total\ weight\ of \ all\ students}}}}{x} = 75.4\)

Next we have that four students added to the class weighing

72.9 kg, 73.8 kg, 79.5 kg and 87.4 kg = 313.6 kg

Now the total number of students will be (x + 4)

And the average weight is increased by 0.24

So the new average weight is 75.4 + 0.24 = 75.64kg

Number of students are given by: 75.64 (x + 4)

So we have:

75.4x + 313.6 = 75.64 x + 75.64 × 4

- 0.24x = 302.56 – 313.6

\(x = \dfrac{11.04}{0.24}= 46\)

so total number of students initially were 46.