CAT Practice : Averages, Ratios, Mixtures

When we mix two mixtures in a particular ratio, we get a third mixture. Given the third mixture how does one find the ratio in which they were mixed.

Alligation

Q.37: What would be the ratio of milk and water in a final mixture formed by mixing milk and water that are present in three vessels of capacity 1l, 2l, and 3l respectively and in the ratios 5:1, 3:2 and 4:3 respectively?
1. 747:443
2. 787:1260
3. 787:473
4. 747:473

Choice C. 787:473

Detailed Solution

Solve this type of questions by taking 2 at a time. Take the first 2 vessels,
In 1st, fraction of milk = $\frac{5}{6}$
In 2nd, fraction of milk = $\frac{3}{5}$
Therefore,

= ) $\frac{\frac{3}{5} - x}{x - \frac{5}{6}} = \frac{1}{2}$
= ) $\frac{6}{5} - 2x = x - \frac{5}{6}$
= ) $\frac{6}{5} + \frac{5}{6} = 3x$
= )$x = \frac{61}{90}$ (And the volume of mixture after mixing = 1 + 2 = 3 l)
Therefore,

= ) $\frac{\frac{4}{7} - x}{x - \frac{61}{90}} = \frac{3}{3}$
= ) $\frac{4}{7} - x = x + \frac{61}{90}$
= ) $\frac{4}{7} + \frac{61}{90} = 2x$
= ) $2x = \frac{787}{630} => x = \frac{787}{1260}$
Therefore, Milk : Water = $\frac{787}{(1260 - 787)} = \frac{787}{473}$

Our Online Course, Now on Google Playstore!

Fully Functional Course on Mobile

All features of the online course, including the classes, discussion board, quizes and more, on a mobile platform.

Cache Content for Offline Viewing

Download videos onto your mobile so you can learn on the fly, even when the network gets choppy!

More questions from Averages, Ratios, Mixtures

Averaages, Ratios and Mixtures XXXXXXXXXXXXXXXXXXXXXXXXXe.