ratio & proportions

by aparna
(chennai)

a man bought 66 kgs of 3 types of fruits namely banana, oranges and apple. The ratio of banana to oranges is 4:5 and that of oranges to apples is 2:3 Find out how many kgs of apples were bought

Let x be number of Banana
Let y be number of orange
let z be number of apple

x + y + z = 66

x/y = 4/5
After cross-multiplication, 5x = 4y.
Thus, x = 4y/5

y/z = 2/3
After cross-multiplication, 2z = 3y.
Thus, z = 3y/2

Replace x and z into x + y + z = 66
4y/5 + y + 3y/2 = 66

(8y + 10y + 15y)/10 = 66

33y/10 = 66

33y = 660, so y = 20
There are 20 kg of oranges

Since z = 3y/2, z = (3 * 20)/2 = 60/2 = 30
There are 30 kg of apples