Question : In two blends of mixed tea, the ratios of Darjeeling to Assam tea are 4 : 7 and 2 : 5. The ratio in which these two blends should be mixed to get the ratio of Darjeeling to Assam tea in the new mixture to 6 : 13 is:
Option 1: 22 : 35
Option 2: 26 : 35
Option 3: 35 : 78
Option 4: 13 : 22
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Correct Answer: 22 : 35
Solution :
The ratios of Darjeeling tea to Assam tea in the two blends are 4 : 7 and 2 : 5.
Darjeeling tea in mixture 1 = $\frac{4}{11}$
Darjeeling tea in mixture 2 = $\frac{2}{7}$
The ratio of Darjeeling tea to Assam tea in the new blend is 6 : 13.
The fraction of the new tea mixture that is Darjeeling is $\frac{6}{19}$.
Now, by the rule of alligation,
The required ratio = $(\frac{6}{19}-\frac{2}{7}):(\frac{4}{11}-\frac{6}{19})$
= $\frac{4}{19×7}:\frac{10}{11×19}$
= $\frac{4}{7}:\frac{10}{11}$
= $22 : 35$
Hence, the correct answer is 22 : 35.
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