the ratio of boys to girls in a class is 5:9 if 19 was added to the boys and 4 was added to the girls the ratio will be 9:7 QUESTION how many was the original number of boys and girls in the class?
let original number of boys be x
let original number of girls be y
number of boys/number of boys = x/y = 5/9
therefore, 9x = 5y ---------------------- equtaion (1)
when 19 boys are added the number of boys become = x+19
when 4 girls are added the number of girls become = y+4
therefore the new raito becomes, x+19/y+4 = 9/7
7(x+19) = 9(y+4)
7x+133 = 9y+36
7x+133-36 = 9y
7x+97 = 9y -------------------- equation(2)
dividing equation (1) & (2)
9x/7x+97 = 5y/9y
9x/7x+97 = 5/9
x = 485/46 = 10.54
since number of boys can not be in decimals so we take as x = 10
now on putting the value of x in equation (1)
9*10 = 5y
y=18
hence the original number of boys in the class is 10 and girls is 18.
Sol ---The ratio of boys to girls in a class is 5:9 . Let the common multiple be X . Therefore the number of boys and girls wil be 5X and 9X
19 was added to the boys and 4 was added to the girls the ratio will be 9:7 .
then the equation becomes 5X + 19 / 9X + 4 = 9/7
On solving you will get the value of X . therefore the no of boys wil be 5X and 9X .
( In this problem , there is some mistake hence we are getting the answer in fraction , but number of boys and girls cant be in fractions . I have just shown the method to solve the problem .)