Question

Tina, Mina, Gina, Lina and Bina are 5 sisters, aged in that order, with Tina being the eldest. Each of them had to carry a bucket of water from a well to their house. Their buckets’ capacities were proportional to their ages. While returning, equal amount of water got splashed out of their buckets. Who lost maximum amount of water as a percentage of the bucket capacity?

• A. Tina
• B. Mina
• C. Gina
• D. Lina
• E. Bina

Hint:

- When equal absolute quantities are removed from unequal totals, the \textit{smaller} total suffers a greater percentage loss.
- Always compare fractions by keeping the numerator constant.

Answer 1

Answer: (E)

Step 1: The problem states that the bucket capacities are proportional to their ages. Since Tina is the eldest, her bucket is the largest, and since Bina is the youngest, her bucket is the smallest.
Step 2: Assume the ages of Tina, Mina, Gina, Lina, and Bina are \(5, 4, 3, 2, 1\) respectively (or in descending order with any proportional ratio). Then, their bucket capacities are also in the ratio \(5:4:3:2:1\).
Step 3: Suppose the equal amount of water lost by each sister is \(x\) liters. Then the fraction of water lost by each is: \[ \text{Fraction lost} = \frac{x}{\text{bucket capacity}}. \]
Step 4: For Tina, fraction lost \(= \frac{x}{5}\). For Mina \(= \frac{x}{4}\). For Gina \(= \frac{x}{3}\). For Lina \(= \frac{x}{2}\). For Bina \(= \frac{x}{1} = x\).
Step 5: Clearly, as the denominator decreases, the fraction lost increases. Hence, Bina (youngest, with the smallest bucket) loses the maximum water as a % of her bucket capacity.
\[ \boxed{\text{Bina loses the maximum percentage of water.}} \]