A vessel contains milk and water in the ratio of 5:4 and 9 litres of mixture is removed from the vessel and replaced

A vessel contains milk and water in the ratio of 5:4 and 9 litres of mixture is removed from the vessel and replaced with 14 litres of water, then the ratio becomes 9:10. Find the final quantity of water in the vessel.

a)            40 litres

b)            45 litres

c)            50 litres

d)            36 litres

e)            None of these

Sol:

Initial quantity of milk = 5x

Initial quantity of water = 4x

(5x – 9*5/9)/(4x – 9*4/9 + 14) = 9/10

(5x – 5)/(4x + 10) = 9/10

x = 10

Initial quantity of water = 4 * 10 = 40 litres

Final quantity of water = 4 * 10 – 4 + 14 = 50

litres