Question

Jack and Jill went up the hill to fetch a pail of water. having filled the pail to the full. Jack fell down, spilling
$\frac{2}{3}$
of water, before Jill caught the pail. She then tumbled down the hill, spilling
$\frac{1}{5}$
of the remainder. what fraction of the water fills the pail?

Answer 1

Total amount of water in pail is basically 1/1


If 2/3 was spilt, we basically subtract 2/3 from 1.

$1 - \frac{2}{3} = \frac{3 - 2}{3} \\ = \frac{1}{3}$
Next, 1/5 of the remainder (which we just calculated, 1/3) was lost. Therefore, we need to first find 1/5 of 1/3 and then subtract that value from 1/3.
$\frac{1}{5} \times \frac{1}{3} = \frac{1}{15 } \\ \frac{1}{3} - \frac{1}{15} = \frac{5 - 1}{15} = \frac{4}{15}$
Therefore 4/15th of the initial water remains in the pail.

Answer 2

yes this is the correct answer