The weight of an empty bucket is 25% of the weight of the bucket when filled with some liquid. Some of the liquid has been removed. Then, the bucket, along with the remaining liquid, weighed three-fifths of the original weight. What percentage of the liquid has been removed?

Question: The weight of an empty bucket is 25% of the weight of the bucket when filled with some liquid. Some of the liquid has been removed. Then, the bucket, along with the remaining liquid, weighed three-fifths of the original weight. What percentage of the liquid has been removed?

Solution:
let, weight of empty bucket is x liter

x = 25% (x + some liquid)
⇒ x = (1/4) (x + some liquid)
⇒ 4x = x + some liquid
⇒ 3x = some liquid
⇒ some liquid = 3x

Then, the bucket, along with the remaining liquid, weighed three-fifths of the original weight.
weight of removed liquid = (2/5) × 4x = 8x/5

%percentage removed = (8x/5/3x ) × 100%
= (160/3)%