A solution A contains alcohol and water in the ratio 1 : 3 and a solution B contains alcohol and water in ratio 4 : 5. If both the solutions are mixed in equal quantities what is the ratio of alcohol and water in the final mixture?

Let amount of alcohol in A = x
Thus, total volume of solution A = x + 3x = 4x
Amount of alcohol in B = 4k
Thus, total volume of solution B = 4k + 5k = 9k
Since, volume of both solutions is equal 4x = 9k (1)
Ratio of alcohol in the final solution = (x + 4k)/(4x + 9k)
On substituting (1) we get ratio of alcohol in the final solution = 25 : 72
Thus, ratio of alcohol and water in the final solution = 25 : 47