The average marks of a class of students are76.The average marks of boys and girls are 69and 83 respectively. If there are 100 boys in the class find the number of girls in the class.
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Answer:
The number of girls are 100
Steps to solve :-
Let number of girls unknown be x
Given the number of boys are 100
( Sum of marks of 100 boys + Sum of marks of x girls ) / ( 100 + x ) = 76
Sum of marks of 100 boys + Sum of marks of x girls = 76 × ( 100 + x ) = 7600 + 76 x ----- ( 1 )
Given the average of 100 boys is 69
==> Sum of marks of 100 boys / 100 = 69
Sum of marks of 100 boys = 69 × 100 = 6900
Given the average of x girls = ( Sum of marks of x girls ) / x = 83
So, Sum of marks of x girls = 83 x
In ( 1 ) ,
6900 + 83 x = 7600 + 76 x
83 x - 76 x = 7600 - 6900
7 x = 700
x = 700 / 7
x = 100
Therefore, the number of girls are also 100
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