Question

9L of water is drawn from a cask which was initially full and is then filled with milk. 9L of the present mixture is again taken out and the cask is again filled with milk. The ratio of the quantity of water now left in the cask to that of the milk is 16 $:$ 9. What is the capacity of the cask?

• A. 30L
• B. 35L
• C. 40L
• D. 45L
• E. 50L

Answer 1

The correct option is D

45L

Let there be x litres in the cask. After n operations:

The quantity in the cask $=x{\left(\frac{x-y}{x}\right)}^n$
Thus, in this case$\frac{x\times {\left(\frac{x-9}{x}\right)}^2}{x}=(\frac{x-9}{x}{)}^2=\frac{16}{25}\frac{x-9}{x}=\frac{4}{5}\therefore x=45litres$