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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 ofĀ acid and water in the firstĀ beaker =Ā 2 : 3
quantity of acidĀ in the first beaker =Ā $$\frac{2}{2+3}$$ =Ā $$\frac{2}{5}$$
quantity of water in the first beakerĀ = $$\frac{3}{2+3}$$Ā = $$\frac{3}{5}$$
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 =Ā $$\frac{2}{5}+\frac{3}{7}$$ :Ā $$\frac{3}{5}+\frac{4}{7}$$
=Ā $$\frac{14+15}{35}:\ \frac{21+20}{35}$$
= $$\frac{29}{35}:\ \frac{41}{35}$$= 29 : 41
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