A bottle contains 20 litres of liquid A. 4 litres of liquid A is taken out of it and replaced by same…
A bottle contains 20 litres of liquid A. 4 litres of liquid A is taken out of it and replaced by same quantity of liquid B. Again 4 litres of the mixture is taken out and replaced by same quantity of liquid B. What is the ratio of quantity of liquid A to that of liquid B in the final mixture?
4 : 1
5 : 1
16 : 9
17 : 8
Solution
After two replacements, the quantity of liquid A remaining $= 20 \times \left(1 - \dfrac{4}{20}\right)^2 = 20 \times \left(\dfrac{4}{5}\right)^2 = 20 \times \dfrac{16}{25} = 12.8$ litres. Liquid B $= 20 - 12.8 = 7.2$ litres. Ratio A : B $= 12.8 : 7.2 = 128 : 72 = 16 : 9$.