The ratio of milk and water in three samples is 1 : 3, 3 : 5, and 11 : 5 (milk : water). Equal quantities of all three samples are mixed together. What will be the final ratio of milk and water in the new mixture?

Introduction:
This question checks mixture averaging using ratios. When we mix equal quantities from different samples, we can compute the final composition by converting each ratio into fractions (milk fraction and water fraction), then averaging those fractions because each sample contributes the same total volume. The key is to avoid directly averaging the ratios (that would be wrong). Instead, convert each sample into milk and water fractions first, then combine.

Given Data / Assumptions:

• Sample 1 milk : water = 1 : 3• Sample 2 milk : water = 3 : 5• Sample 3 milk : water = 11 : 5• Equal quantities of all three samples are mixed

Concept / Approach:
If each sample contributes the same total quantity (say 1 unit each), then total milk in final mixture = sum of milk fractions from each sample, and total water = sum of water fractions. Finally, convert total milk : total water into simplest integer ratio.

Step-by-Step Solution:
Step 1: Convert each ratio to a milk fraction.For 1 : 3, total parts = 1+3 = 4, milk fraction = 1/4, water fraction = 3/4For 3 : 5, total parts = 8, milk fraction = 3/8, water fraction = 5/8For 11 : 5, total parts = 16, milk fraction = 11/16, water fraction = 5/16Step 2: Assume 1 unit of each sample is taken.Total milk = 1/4 + 3/8 + 11/16Convert to common denominator 16: 1/4 = 4/16, 3/8 = 6/16, so total milk = (4+6+11)/16 = 21/16Total mixture quantity = 3 units, so milk fraction in mixture = (21/16) / 3 = 21/48 = 7/16Step 3: Water fraction = 1 - 7/16 = 9/16Therefore milk : water = 7/16 : 9/16 = 7 : 9

Verification / Alternative check:
You can also add total water fractions directly: 3/4 + 5/8 + 5/16 = 12/16 + 10/16 + 5/16 = 27/16. Dividing by 3 gives water fraction = (27/16)/3 = 27/48 = 9/16, matching our result. So the ratio 7 : 9 is consistent.

Why Other Options Are Wrong:
5 : 7 and 9 : 11 suggest a different milk fraction (around 0.41), but actual milk fraction is 7/16 = 0.4375.9 : 7 reverses the dominance; water is actually more than milk here.15 : 13 is close to 1 : 1, which is not possible given two samples are water-heavy.

Common Pitfalls:
• Averaging ratios directly instead of converting to fractions.• Forgetting that samples are mixed in equal quantities.• Making arithmetic errors while using common denominators.

Final Answer:
The ratio of milk to water in the new mixture is 7 : 9.