A vessel contains 90 litres of mixture of Apple juice and Orange juice in the ratio of 5:4 and 6x litres of mixture is

A vessel contains 90 litres of mixture of Apple juice and Orange juice in the ratio of 5:4 and 6x litres of mixture is removed from the vessel and 4x litres of Orange juice is added to the vessel and the ratio of Apple juice and Orange juice becomes 10:11. Find the value of ‘x’.

a.            5 litres

b.            8 litres

c.             3 litres

d.            10 litres

e.            None of these

Sol:

Initial quantity of Apple juice = 90 * 5/9 = 50 litres

Initial quantity of Orange juice = 90 * 4/9 = 40 litres

6x litres of mixture is removed and 4x litres of orange juice is added and ratio becomes 10:11

(50 – 6x*5/9)/(40 – 6x*4/9 + 4x) = 10/11

(150 – 10x)/(120 + 4x) = 10/11

1650 – 110x = 1200 + 40x

450 = 150x

x = 3 litres