in a particular class there are 40 students .in a test,a mean mark scored by the students of the class is 70.the mean mark scored by the boys is 55 while that of the girls is 75.what are respective number of boys and girls

Dear Student,
Let the number of boys be "x" and number of girls be "y"
​​​​​​Since, Total number of students in Class is 40

Thus, x+y=40               
i.e. x = 40-y                        ............1

$$\begin{gathered} \mathrm{Since}, \mathrm{Mean} \mathrm{Marks} \mathrm{of} \mathrm{Boys} = 55 \\ \mathrm{Thus}, \mathrm{Total} \mathrm{Marks} \mathrm{Scored} \mathrm{by} \mathrm{Boys} = (\mathrm{No}. \mathrm{of} \mathrm{Boys}) \mathrm{X} (\mathrm{Mean} \mathrm{Marks} \mathrm{of} \mathrm{Boys}) = 55\mathrm{x} \\ \mathrm{And}, \mathrm{Mean} \mathrm{Marks} \mathrm{of} \mathrm{Girls} = 75 \\ \mathrm{Thus}, \mathrm{Total} \mathrm{Marks} \mathrm{Scored} \mathrm{by} \mathrm{Girls} = (\mathrm{No}. \mathrm{of} \mathrm{Girls} ) \mathrm{X} (\mathrm{Mean} \mathrm{Marks} \mathrm{of} \mathrm{Girls} ) = 75\mathrm{y} \\ \mathrm{Also}, \mathrm{Mean} \mathrm{Marks} \mathrm{of} \mathrm{Class} = 70 \\ \mathrm{Thus}, \mathrm{Total} \mathrm{Marks} \mathrm{Scored} \mathrm{by} \mathrm{Class} = (\mathrm{Total} \mathrm{Students} ) \mathrm{X} (\mathrm{Mean} \mathrm{Marks} \mathrm{of} \mathrm{Class}) = 40\left(70\right) \\ \mathrm{Total} \mathrm{Marks} \mathrm{Scored} \mathrm{by} \mathrm{Class} = 2800 \\ \mathrm{But} , \mathrm{Total} \mathrm{Marks} \mathrm{Scored} \mathrm{by} \mathrm{Class} = \mathrm{Marks} \mathrm{Scored} \mathrm{by} \mathrm{Boys} + \mathrm{Marks} \mathrm{Scored} \mathrm{by} \mathrm{Girls} \\ \Rightarrow 55\mathrm{x}+75\mathrm{y}=2800 \\ \Rightarrow 55(40-\mathrm{y})+75\mathrm{y}=2800 \\ \Rightarrow 2200-55\mathrm{y}+75\mathrm{y}=2800 \\ \Rightarrow 20\mathrm{y}=600 \\ \Rightarrow \mathrm{y}=30 \\ \mathrm{Using} 1 \\ \Rightarrow \mathrm{x}=40-\mathrm{y}=40 -30 \\ \Rightarrow \mathrm{x}=10 \end{gathered}$$

Thus, he number of boys are "10" and number of girls are "30"
Regards