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

Since, Mean Marks of Boys = 55  Thus, Total Marks Scored by Boys = (No. of Boys) X (Mean Marks of Boys) = 55x  And, Mean Marks of Girls = 75  Thus, Total Marks Scored by Girls = (No. of Girls ) X (Mean Marks of Girls ) = 75y  Also, Mean Marks of Class = 70  Thus, Total Marks Scored by Class = (Total Students ) X (Mean Marks of Class) = 40(70)  Total Marks Scored by Class = 2800   But , Total Marks Scored by Class = Marks Scored by Boys + Marks Scored by Girls   55x+75y=2800  55(40-y)+75y=2800  2200-55y+75y=2800  20y=600  y=30 Using 1  x=40-y=40 -30 x=10  

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

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