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Question : A vessel is filled with liquid, 5 parts of which are water and 11 parts syrup. What part of the mixture must be drawn off and replaced with water so that the mixture may be syrup and water in the ratio 3 : 2?

Option 1: $\frac{14}{45}$

Option 2: $\frac{27}{35}$

Option 3: $\frac{36}{65}$

Option 4: $\frac{7}{55}$


Team Careers360 16th Jan, 2024
Answer (1)
Team Careers360 24th Jan, 2024

Correct Answer: $\frac{7}{55}$


Solution : 5 parts water and 11 parts syrup (considering the unit volume of the mixture)
Water = $\frac{5}{16}$ and syrup = $\frac{11}{16}$
Let $x$ amount of liquid is replaced by water.
Water = $\frac{5x}{16}$ and syrup = $\frac{11x}{16}$
According to the question,
$\frac{\frac{11}{16}-\frac{11x}{16}}{\frac{5}{16}+x-\frac{5x}{16}}=\frac{3}{2}$
Or, $\frac{\frac{11}{16}-\frac{11x}{16}}{\frac{5}{16}+\frac{11x}{16}}=\frac{3}{2}$
Or, $\frac{15}{16}+\frac{33x}{16}=\frac{22}{16}-\frac{22x}{16}$
Or, $33x+22x=22-15$
Or, $x=\frac{7}{55}$
Hence, the correct answer is $\frac{7}{55}$.

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