SSC Sample Paper Mock Test-8 SSC CGL Tear-II Paper-1

A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?

A) \[\frac{1}{3}\]

B) \[\frac{1}{4}\]

C) \[\frac{1}{5}\]

D) \[\frac{1}{7}\]

Correct Answer: C

Solution :

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 \[=\left( \frac{1}{8}\text{of}\frac{8}{5} \right)=\frac{1}{5}\]