smc

Question

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

Accepted Answer

The amount of alcohol in the jars are pp+1 and qq+1, and the amount of water in the jars are 1p+1 and 1q+1. Then the total amount of alcohol is pp+1 + qq+1 = p+q+2pq(p+1)(q+1), and the total amount of water is 1p+1 and 1q+1 = p+q+2(p+1)(q+1). The ratio of the volume of alcohol to the volume of water in the mixture is p+q+2pq(p+1)(q+1)p+q+2(p+1)(q+1) = p+q+2pqp+q+2.