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, 79.5 kg and 87.4 kg 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?

Let number of students initially be n 
Now Sum of weight of students initially will be n(average weight ) = 75.4n    (1)
Now 4 new students joined
Now sum of weights of 4 students = 72.9+73.8+79.5+87.4 = 313.6
Now total sum becomes 75.4n+313.6    (2)
Now new average given as 75.4+0.24 = 75.64     (3)
Now we can say $$75.64\ =\frac{75.24n+313.6}{n+4}$$
we get 75.64n +302.56 =75.24n+313.6
we get 0.24n =11.04
we get n = 11.04/0.24
we get n = 46