Question

Two identical jars are filled with alcohol solutions. The ratio of the volume of alcohol to the volume of water is $p:1$ in one jar and $q:1$ in the other jar. If the entire contents of the two jars are mixed/ together, then what is the ratio of the volume of alcohol to the volume of water in the mixture?

• A. $\frac{p+q+2pq}{p+q+2}$
• B. $\frac{p+q}{p+q+2}$
• C. $\frac{p+q+1}{p+q+2}$
• D. None of these

Answer 1

The correct option is A $\frac{p+q+2pq}{p+q+2}$

If each jar contains a total of x liters of solution, then one jar contains $\frac{px}{p+1}$ liters of alcohol and $\frac{x}{p+1}$ liters of water.
The other jar contains $\frac{qx}{q+1}$ liters of alcohol and $\frac{x}{q+1}$ liters of water.
Therefore, the ratio of the volume of alcohol to the volume ofwater in the mixture is then
$=\frac{[\frac{p}{p+1}+\frac{q}{q+1}]x}{[\frac{1}{p+1}+\frac{1}{q+1}]x}=\frac{p(q+1)+q(p+1)}{(q+1)+(p+1)}=\frac{p+q+2pq}{p+q+2}$