A) \[\frac{1}{3}\]
B) \[\frac{1}{4}\]
C) \[\frac{1}{5}\]
D) \[\frac{1}{7}\]
Correct Answer: C
Solution :
[c] Let the vessel initially contain 8 L of liquid. Let x L of this liquid be replaced with water. Quantity of water in the new mixture \[=\left( 3-\frac{3x}{8}+x \right)L\] Quantity of syrup in the new mixture \[=\left( 5-\frac{5x}{8} \right)L\] \[\therefore \] \[3-\frac{3x}{8}+x=5-\frac{5x}{8}\] \[\Rightarrow \] \[24-3x+8x=40-5x\] \[\Rightarrow \] \[10x=16\] \[\Rightarrow \] \[x=\frac{16}{10}=\frac{8}{5}\] Part of the mixture replaced \[=\left( \frac{1}{8}\,\,\text{of}\,\,\frac{8}{5} \right)=\frac{1}{5}\] |
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