Question : One cup has juice and water in the ratio 5 : 2, while another cup of the same capacity has them in the ratio 7 : 4, respectively. If the contents of both the cups (when full) are poured into a vessel, then what will be the final ratio of water to juice in the vessel?
Option 1: 52 : 25
Option 2: 25 : 52
Option 3: 26 : 25
Option 4: 25 : 26
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Correct Answer: 25 : 52
Solution :
The ratio of one cup of juice and water = 5 : 2
The ratio of another cup of the same capacity has them = 7 : 4
The juice in the one cup = $\frac{5}{7}$
The water in the one cup = $\frac{2}{7}$
The juice in the another cup = $\frac{7}{11}$
The water in the another cup = $\frac{4}{11}$
When the contents of both cups are poured into a vessel, the ratio will be:
Juice : Water
= $\frac{5}{7}+\frac{7}{11} : \frac{2}{7}+\frac{4}{11}$
= $\frac{55+49}{77} : \frac{22+28}{77}$
= $\frac{104}{77} : \frac{50}{77}$
= $104:50$
= $52:25$
The final ratio of water to juice in the vessel = (25 : 52)
Hence, the correct answer is 25 : 52.
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