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Three containers have their volumes in the ratio 3:4:5. They are full of milk and water. The mixtures contain milk and water in the ratios of 4:1, 3:1 and 5:2, respectively. Find the ratio of milk and water in the fourth container which contains all these mixtures.

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41 : 14

151 : 48

157 : 53

15 : 32

answer is C.

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Detailed Solution

Given,
The three containers of volumes ratio = 3:4:5
Suppose volumes of containers = 3x, 4x, 5x respectively.
Container whose volume is 3x, consist the amount of milk,

Milk = \frac{4}{4 + 1} \times 3 x

Water = \frac{1}{4 + 1} \times 3 x

Container whose volume is 4x, consist the amount of milk,

Milk = \frac{3}{3 + 1} \times 4 x

Water = \frac{1}{3 + 1} \times 4 x

Container whose volume is 5x, consist the amount of milk,
Milk

= \frac{5}{5 + 2} \times 5 x

Water

= \frac{2}{5 + 2} \times 5 x

So, overall milk

= \frac{12}{5} x + \frac{12}{4} x + \frac{25}{7} x

= \frac{1256}{140} x

Also, overall water

= \frac{3}{5} x + \frac{4}{4} x + \frac{10}{7} x

= \frac{424}{140} x

In the fourth container in milk to water ratio,

= \frac{1256}{424}

= 157 : 53

Thus, the option 3 is correct.

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