Question

There are three containers of equal capacity and all are completely filled with mixtures of acid & water in different ratios. The ratio of acid to water in the first container is 2:3, in the second container the ratio is 3:7 and in the third container it is 4:11. If the mixture of all three containers are mixed together, find the ratio of acid to water.

Answer 1

Let the volume of each contained be 100 cc.
Hence the volume of acid in each of the container $=\frac{2}{5}\times 100,\frac{3}{10}\times 100\&\frac{4}{15}\times 100cc$ respectively.
The total volume of acid in the three containers $=\frac{2}{5}\times 100+\frac{3}{10}\times 100+\frac{4}{15}\times 100=\frac{290}{3}cc.$
Similarly volume of water in each of the container $=\frac{3}{5}\times 100,\frac{7}{10}\times 100\&\frac{11}{15}\times 100cc$ respectively.
So when contents of all 3 are mixed together, the total volume of water $=\frac{3}{5}\times 100+\frac{7}{10}\times 100+\frac{11}{15}\times 100=\frac{610}{3}cc.$
Hence, ratio of acid to water in the mixture $=\frac{290}{3}:\frac{610}{3}=29:61$