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,

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?​

Answer 1

Initially $46$ number of students in the group.

Step-by-step explanation:

Given,

The average weight of the students in  a group was $75.4\ kg$ and later on four students having weights $72.9\ kg, 73.8\ kg,79.5\ kg\ and\ 87.4\ kg$ joined the group.

Lets Initially $x$ number of students there.

Average weight of four students is$=\frac{72.9+73.8+79.5+87.4}{4}$

                                                         $=78.4\ kg$

Now total students $=(x+4)$

Average weight of $(x+4)$ students is$=\frac{75.4x+72.9+73.8+79.5+87.4}{x+4}$

                                                             $=\frac{75.4x+313.6}{x+4}$  $kg$

From given statements,

∴ $\frac{75.4x+313.6}{x+4}-75.4=0.24$

⇒$\frac{75.4x+313.6}{x+4}=0.24+75.4$

⇒$\frac{75.4x+313.6}{x+4}=75.64$

⇒$75.4x+313.6=75.64x+302.56$

⇒$75.64x-75.4x=313.6-302.56$

⇒$0.24x=11.04$

⇒$x=\frac{11.04}{0.24}$

⇒$x=46$

So, Initially $46$ number of students in the group.

                                                         

Answer 2

Answer:

46

Step-by-step explanation:

Deviation method

Deviation from 75.4kg

(75.4-72.9)= -2.5

75.4-73.8= -1.6

79.5-75.4= +4.1

87.4-75.4= +12

Let the initial number of students be x,4 people have joined. Therefore, it becomes (x+4)

(-2.5-1.6+4.1+12)/ (x+4 )= 0.240

12/(x+ 4 )= 0.240

12/0.240= x+4

x= 46