Question

When 6 new boys were admitted and 6 girls left from the class the percentage of girls decreased fr 68% to 56% find the original number of boys and girls?

Answer 1

let total no. of girls be x & boys be y

total class strength = x+y

percentage of girls initially= x/x+y = 0.68

x=0.68x + 0.68 y

=> x - 0.68x = 0.68y

=> 0.32 x= 0.68 y

=> x= 2.125y-----------------------------(1)

after 6 girls left, total no. of girls= x-6

simultaneously, 6 boys joined, so total strength remained unchanged

percentage of girls after 6 left = x-6/x+y = 0.56

x-6 = 0.56x + 0.56 y

=>x - 0.56 x - 6= 0.56 y

=> 0.44x - 0.56 y= 6 ----------------------------(2)

(1) in (2)

=> 0.935 y- 0.56 y=6

=>0.375 y= 6

=>y = 6/0.375 = 16

therefore no. of boys are 16

no. of girls= 2.125 * 16 = 34

girls= 34 & boys= 16