Question 80

# Consider three mixtures — the first having water and liquid A in the ratio 1:2, the second having water and liquid B in the ratio 1:3, and the third having water and liquid C in the ratio 1:4. These three mixtures of A, B, and C, respectively, are further mixed in the proportion 4: 3: 2. Then the resulting mixture has

Solution

The proportion of water in the first mixture is $$\frac{1}{3}$$
The proportion of Liquid A in the first mixture is $$\frac{2}{3}$$

The proportion of water in the second mixture is $$\frac{1}{4}$$
The proportion of Liquid B in the second mixture is $$\frac{3}{4}$$

The proportion of water in the third mixture is $$\frac{1}{5}$$
The proportion of Liquid C in the third mixture is $$\frac{4}{5}$$

As they are mixed in the ratio 4:3:2, the final amount of water is $$4 \times \frac{1}{3} + 3 \times \frac{1}{4} + 2 \times \frac{1}{5} = \frac{149}{60}$$
The final amount of Liquid A in the mixture is $$4\times\frac{2}{3} = \frac{8}{3}$$
The final amount of Liquid B in the mixture is $$3\times\frac{3}{4} = \frac{9}{4}$$
The final amount of Liquid C in the mixture is $$2\times\frac{4}{5} = \frac{8}{5}$$

Hence, the ratio of Water : A : B : C in the final mixture is $$\frac{149}{60}:\frac{8}{3}:\frac{9}{4}:\frac{8}{5} = 149:160:135:96$$

From the given choices, only option C  is correct.

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