Question : Three glasses of equal volumes contain acid mixed with water. The ratios of acid to water are 2 : 3, 3 : 4, and 4 : 5, respectively. The contents of these glasses are poured into a large vessel. The ratio of acid to water in the large vessel is:
Option 1: 411 : 540
Option 2: 401 : 544
Option 3: 417 : 564
Option 4: 407 : 560
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Correct Answer: 401 : 544
Solution :
The ratios of acid to water in three equal glasses are 2 : 3, 3 : 4, and 4 : 5, respectively.
On mixing all three mixtures,
Acid = $\frac{2}{5}+\frac{3}{7}+\frac{4}{9}$
= $\frac{126+135+140}{315}$
= $\frac{401}{315}$
Water = $\frac{3}{5}+\frac{4}{7}+\frac{5}{9}$
= $\frac{189+180+175}{315}$
= $\frac{544}{315}$
$\therefore$ Required ratio = $\frac{401}{315}$ : $\frac{544}{315}$ = 401 : 544
Hence, the correct answer is 401 : 544.
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