Question : Mixture A contains chocolate and milk in the ratio 4 : 3 and mixture B contains chocolate and milk in the ratio 5 : 2. A and B are taken in the ratio 5 : 6 and mixed to form a new mixture. The percentage of chocolate in the new mixture is closest to:
Option 1: 35%
Option 2: 69%
Option 3: 31%
Option 4: 65%
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Correct Answer: 65%
Solution :
The ratio of chocolate to milk in mixture A = 4 : 3
The ratio of chocolate to milk in mixture B = 5 : 2
Let 5 units taken from mixture A and 6 units taken from mixture B.
The ratio of chocolate to milk in new mixture = $(5\times \frac{4}{7} + 6\times \frac{5}{7}):(5\times \frac{3}{7} + 6\times \frac{2}{7})$ = 50 : 27
Percentage of chocolate in new mixture = $\frac{\text{chocolate}}{\text{chocolate + milk}} \times 100$
= $\frac{50}{(50 + 27)} \times 100$
= 64.93%
= 65% (approx)
Hence, the correct answer is 65%.
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