Question : Container I and Container II have milk and water in the ratio of 4 : 5 and 8 : 3 respectively. In what ratio Container I and Container II should be mixed to get a new mixture in which milk and water are in the ratio of 9 : 11?
Option 1: 519 : 11
Option 2: 49 : 121
Option 3: 549 : 11
Option 4: 47 : 121
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Correct Answer: 549 : 11
Solution :
Given: Container I and Container II have milk and water in the ratio of 4: 5 and 8: 3 respectively.
Quantity 1 in the mixture = $\frac{\text{Quantity 1}}{\text{Quantity 1 + Quantity 2}}$
In the first mixture, the milk = $\frac{4}{(4 + 5)} = \frac{4}{9}$
The second mixture's milk = $\frac{8}{(8 + 3)} = \frac{8}{11}$
The new mixture's milk = $\frac{9}{(9 + 11)} = \frac{9}{20}$
The mixture's ratio = $(\frac{8}{11}–\frac{9}{20}):(\frac{9}{20}–\frac{4}{9})$
⇒ $\frac{160–99}{11\times20}:\frac{81–80}{20\times 9}= \frac{61}{11\times20}:\frac{1}{20\times 9}=549:11$
Hence, the correct answer is 549 : 11.
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