In a class, 50% of the students are boys. Of the girls, 45% are good at physics, 65% are good at chemistry and 60% are good at
maths. 30% are good at physics and chemistry, 35% are good at chemistry and maths and 25% are good at physics and maths.
Given that all the girls are good at least one of the three subjects mentioned, what is the number of girls who are good in all the three
subjects if there are 100 students in the class?
A) 10
B) 20
C) 8
D) 6

• answer should be 22 (as girls cannot be 22.5)
• 12 years agoHelpfull: Yes(2) No(2)
• total students =100
  number of boys = 50
  number of girls = 50
  let no. of girls
  good in physics = x =45%of 50 =22.5
  good in chemistry = y =65%of 50=32.5
  good in maths = z = 60% of 50 = 30
  according to problem
  x+y = 30%of 50 =15 ------------(i)
  y+z = 35%of 50 = 17.5------------( ii )
  z+x =25% of 50 = 12.5------------( iii)
  --------------------------------------…
  2x+2y+2z = 45 (sum i,ii,&iii)
  x+y+z = 22.5 -------------(iv) (it means 5 girl good in one subject only)
  subtract eq.(i) from eq(iv)
  z =7.5
  subtract eq(ii)from eq. (iv)
  x = 5
  subtract eq.(iii)from eq. (iv)
  y = 10
  there fore atleast 5 girls are good in all three subjects.answer
• 12 years agoHelpfull: Yes(1) No(7)