Question

Each boy contribute rupees equal to the number of girls and each girl contribute rupees equal to the number of boys in a class of 60 students. If the total contribution collected is Rs.1600,how many girls are there in the class ?

Answer 1

Let the Number of Boys in the Class be : B

Let the Number of Girls in the Class be : G

Given : Each Boy contributes Rupees Equal to the Number of Girls in the Class

⇒ The Amount of Money Contributed by One Boy is : G Rupees

⇒ The Amount of Money Contributed by 'B' Boys is : (B × G) Rupees

Given : Each Girl contributes Rupees Equal to the Number of Boys in the Class

⇒ The Amount of Money Contributed by One Girl is : B Rupees

⇒ The Amount of Money Contributed by 'G' Girls is : (G × B) Rupees

Given : The Total Number of Students in the Class = 60

⇒ B + G = 60

⇒ B = 60 - G

Given : The Total Contribution Collected is Rs. 1600

⇒ (B × G) + (G × B) = 1600

⇒ BG + BG = 1600

⇒ 2BG = 1600

⇒ BG = 800

But : B = 60 - G

⇒ (60 - G)(G) = 800

⇒ G² - 60G + 800 = 0

⇒ G² - 40G - 20G + 800 = 0

⇒ G(G - 40) - 20(G - 40) = 0

⇒ G = 40 or G = 20

⇒ The Number of Girls in the Class can be : 40 (or) 20

Answer 2

Number boys 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

The number of boys in the

class = 40 or 20