Two vessels contain spirit and water mixed respectively in the ratio of 2 : 1 and 3 : 7. Find the ratio in which these are to be mixed to get a new mixture in which the ratio of spirit to water is 7: 9.
Solution
Correct Answer: Option B
Vessel 1:
Spirit : water = 2:1
∴ Quantity of spirit = \(\frac{2}{{2 + 1}}\)
∴ quantity of spirit in one unit = 2/3
Similarly, quantity of water in one unit = 1/3
Vessel 2:
Spirit : water = 3:7
Therefore quantity of spirit in one unit = \(\frac{3}{{10}}\)
And quantity of water in one unit= \(\frac{7}{{10}}\)
Let vessel 1 and vessel 2 contents be mixed in the ratio x : y
Thus according to the new condition, spirit : water = 7 : 9
\(\frac{{\left( {x \times \frac{2}{3}} \right)\; + \left( {y \times \;\frac{3}{{10}}} \right)}}{{\left( {x \times \frac{1}{3}} \right) + \left( {y \times \frac{7}{{10}}} \right)}} = \frac{7}{9}\)
\(\frac{x}{y} = \;\frac{3}{5}\)
Thus the contents of vessel 1 and 2 should be mixed in the ratio 3 : 5
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