Three liquids having relative densities 2d, 2d and 3d are mixed together in equal proportions by weight. Find the relative density of the resulting mixture.

11d/7
18d/11
13d/9
23d/18

Correct answer: 18d/11

Solution

For equal masses m of each liquid, total mass = 3m. Volumes add: V = m/(2d) + m/(2d) + m/(3d) = m(1/2 + 1/2 + 1/3)/d = m(11/6)/d. Mixture density = 3m / V = 3m / (11m/(6d)) = 18d/11.

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