Two beakers contain acid and water in the ratio 2 : 3 and 3 : 4 respectively. If equal volumes of the mixtures from these two beakers are poured into a common beaker, find the resultant ratio of acid to water in the mixture in the common beaker.

Two beakers contain acid and water in the ratio 2 : 3 and 3 : 4 respectively.

ratio of acid and water in the first beaker = 2 : 3

quantity of acid in the first beaker = $$\frac{2}{2+3}$$ = $$\frac{2}{5}$$

quantity of water in the first beaker = $$\frac{3}{2+3}$$ = $$\frac{3}{5}$$

ratio of acid and water in the second beaker = 3 : 4

quantity of acid in the second beaker = $$\frac{3}{3+4}$$ = $$\frac{3}{7}$$

quantity of water in the second beaker = $$\frac{4}{3+4}$$ = $$\frac{4}{7}$$

If equal volumes of the mixtures from these two beakers are poured into a common beaker, then the resultant ratio of acid to water in the mixture in the common beaker = $$\frac{2}{5}+\frac{3}{7}$$ : $$\frac{3}{5}+\frac{4}{7}$$

= $$\frac{14+15}{35}:\ \frac{21+20}{35}$$