Question : 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.
Option 1: 7 : 5
Option 2: 21 : 29
Option 3: 5 : 7
Option 4: 29 : 41
Correct Answer: 29 : 41
Solution :
Let the volume of the mixture from each beaker be V.
In the first beaker, the ratio of acid to water is 2 : 3.
The volume of acid = $\frac{2}{2+3}V = \frac{2}{5}V$
The volume of water = $\frac{3}{2+3}V = \frac{3}{5}V$
In the second beaker, the ratio of acid to water is 3 : 4.
The volume of acid = $\frac{3}{3+4}V = \frac{3}{7}V$
The volume of water = $\frac{4}{3+4}V = \frac{4}{7}V$
The resultant ratio of acid to water in the mixture in the common beaker,
$=\frac{2}{5}V + \frac{3}{7}V:\frac{3}{5}V + \frac{4}{7}V$
$=\frac{29}{35}V:\frac{41}{35}V$
$= 29 : 41$
Hence, the correct answer is 29 : 41.
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