in a ckass of 60 students each boy contributes rupees equal to number of girls and each girl contributes rupees equal to the number of boys if the total amount is 1600 then how many girls and boys are there in class
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Answer:
Number boys and girls in the
class = 40 or 20
Step-by-step explanation:
Let the number of boys in the class = x
The number of girls in the class = y
the number of students in the
class = 60
x + y = 60 -----( 1 )
Given that each boy contributed
rupees is equal to number of
girls and each girl contributed
Rupees is equal to number of
boys
xy + xy = 1600
=> 2xy = 1600
=> xy = 1600/2
=> y = 800/x --- ( 2 )
From ( 1 ) & ( 2 ) , we get
x + ( 800/x ) = 60
=> x² + 800 = 60x
=> x² - 60x + 800 = 0
=> x² - 40x - 20x + 800 = 0
=> x( x - 40 ) - 20( x - 40 ) = 0
=> ( x - 40 )( x - 20 ) = 0
=> x - 40 = 0 Or x - 20 = 0
=> x = 40 or x = 20
Number boys and girls in the
class = 40 or 20
Step-by-step explanation:
Let the number of boys in the class = x
The number of girls in the class = y
the number of students in the
class = 60
x + y = 60 -----( 1 )
Given that each boy contributed
rupees is equal to number of
girls and each girl contributed
Rupees is equal to number of
boys
xy + xy = 1600
=> 2xy = 1600
=> xy = 1600/2
=> y = 800/x --- ( 2 )
From ( 1 ) & ( 2 ) , we get
x + ( 800/x ) = 60
=> x² + 800 = 60x
=> x² - 60x + 800 = 0
=> x² - 40x - 20x + 800 = 0
=> x( x - 40 ) - 20( x - 40 ) = 0
=> ( x - 40 )( x - 20 ) = 0
=> x - 40 = 0 Or x - 20 = 0
=> x = 40 or x = 20
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