An adulterated milk sample weighs 66 kg with milk : water = 5 : 1. How much water must be added to make the ratio 5 : 3 (milk : water)?

Introduction / Context:Adding only water increases the water quantity while milk remains constant. Set up the ratio with fixed milk to compute the extra water required for the new ratio.

Given Data / Assumptions:

• Total = 66 kg; milk : water = 5 : 1 initially.
• Initial milk = 55 kg; initial water = 11 kg.
• Target milk : water = 5 : 3.

Concept / Approach:Let y be water added. Then water becomes 11 + y. Milk remains 55. Use 55 : (11 + y) = 5 : 3.

Step-by-Step Solution:55 : (11 + y) = 5 : 33*55 = 5*(11 + y)165 = 55 + 5y ⇒ 110 = 5y ⇒ y = 22 kg

Verification / Alternative check:New water = 33 kg; milk : water = 55 : 33 = 5 : 3; total becomes 88 kg, consistent.

Why Other Options Are Wrong:24.750, 16.500, and 20 do not lead to a water total of 33 kg; only 22 kg satisfies the ratio condition.

Common Pitfalls:Accidentally changing milk or targeting milk : total instead of milk : water.

Final Answer:22 kg