A) 18 L
B) 24 L
C) 32 L
D) 42 L
Correct Answer: B
Solution :
| [b] Initially, let the quantity of wine in the cask be x L. Quantity of wine left in cask after 4 operation \[=\left\{ x{{\left( 1-\frac{8}{x} \right)}^{4}} \right\}\,\,L\] \[\therefore \] \[\frac{x{{\left( 1-\frac{8}{x} \right)}^{4}}}{x}=\frac{16}{81}\] \[\Rightarrow \] \[{{\left( 1-\frac{8}{x} \right)}^{4}}={{\left( \frac{2}{3} \right)}^{4}}\] \[\Rightarrow \] \[1-\frac{8}{x}=\frac{2}{3}\]\[\Rightarrow \]\[\frac{8}{x}=\frac{1}{3}\]\[\Rightarrow \]\[x=24\] \[\therefore \] Required quantity = 24 L |
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