Question

Bottle 1 contains a mixture of milk and water in 7 : 2 ratio and Bottle 2 contains a mixture of milk and water in 9 : 4 ratio. In what ratio of volumes should the liquids in Bottle 1 and Bottle 2 be combined to obtain a mixture of milk and water in 3 : 1 ratio?

• A. 27 : 14
• B. 27 : 13
• C. 14 : 27
• D. 27 : 16
• E. 17 : 27

Hint:

Use alligation method for mixture problems: $\frac{\text{Volume 1}}{\text{Volume 2}} = \frac{\text{Difference of higher and desired}}{\text{Difference of desired and lower}}$.

Answer 1

The Correct Option is B

Step 1: Bottle 1: milk fraction = $\frac{7}{9}$, water fraction = $\frac{2}{9}$. Bottle 2: milk fraction = $\frac{9}{13}$, water fraction = $\frac{4}{13}$. Desired mixture: milk fraction = $\frac{3}{4}$, water fraction = $\frac{1}{4}$.
Step 2: Using alligation for milk: Ratio of Bottle 1 to Bottle 2 = $\frac{\frac{9}{13} - \frac{3}{4}}{\frac{3}{4} - \frac{7}{9}}$.
Step 3: $\frac{9}{13} - \frac{3}{4} = \frac{36 - 39}{52} = -\frac{3}{52}$. $\frac{3}{4} - \frac{7}{9} = \frac{27 - 28}{36} = -\frac{1}{36}$.
Step 4: Ratio = $\frac{3/52}{1/36} = \frac{3}{52} \times \frac{36}{1} = \frac{108}{52} = \frac{27}{13}$.
Step 5: So ratio is 27 : 13.
Step 6: Final Answer: 27 : 13.