Question : Milk and water in two vessels A and B are in the ratio 5 : 3 and 2 : 3, respectively. In what ratio should the liquids in both vessels be mixed to obtain a new mixture in vessel C containing half milk and half water?
Option 1: 3 : 4
Option 2: 4 : 5
Option 3: 2 : 3
Option 4: 3 : 5
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Correct Answer: 4 : 5
Solution :
Given: 1st vessel contains milk and water in a ratio of 5 : 3.
2nd vessel contains milk and water in a ratio of 2 : 3.
Milk contains in 1st vessel = $\frac{5}{8}$
Milk contains in 2nd vessel = $\frac{2}{5}$
In the new mixture, both vessels were added in a ratio of 1 : 1.
So, milk contains in new mixture = $\frac{1}{2}$
$\therefore$ The ratio for the new mixture = $\frac{1}{10}:\frac{1}{8}$ = 8 : 10 = 4 : 5
Hence, the correct answer is 4 : 5.
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