Question

An empty pool being filled with water at a constant rate takes 8 hours to fill to $\dfrac{3}{5}$ of its capacity. How much more time will it take to finish filling the pool?
A) $5{\text{ hr 30 min}}$
B) $5{\text{ hr 20 min}}$
C) $4{\text{ hr 48 min}}$
D) $3{\text{ hr 12 min}}$
E) $2{\text{ hr 48 min}}$

Answer 1

Hint: In this question, we know that the pool is filling at a constant rate so the best mathematical approach to solve this question is the ratio method. So using the ratio method we will solve this problem.

Complete step-by-step answer:
The pool is filled to $\dfrac{3}{5}$ of its capacity in the time period of 8 hrs.
Then to fill whole part of the pool = $\dfrac{8}{\dfrac{3}{5}}{\text{ = }}\dfrac{{40}}{3}{\text{ hrs}}$
Now we know the whole part of the pool can be filled in $\dfrac{{40}}{3}$ hrs.
So, we can easily calculate the remaining time to fill the remaining part of the pool.
Let remaining time be $x$
Then,
$x + 8 = \dfrac{{40}}{3}$
By simplifying we will get,
$x{\text{ = }}\dfrac{{40}}{3}{\text{ - 8}}$
By cross multiplying we will get,
$\dfrac{{40 - 24}}{3}$
$
   = {\text{ }}\dfrac{{16}}{3}{\text{ hrs}}{\text{.}} \\
   = {\text{ 5}}\dfrac{1}{3}{\text{ hrs}}{\text{.}} \\
   \Rightarrow {\text{ 5 hrs 20 minutes}}{\text{.}} \\
 $
$\therefore $ Option B is correct.

Note: In this particular question, we have to use the ratio method. In this question, first we will simplify the ratio and then by using cross – multiply we will get our answer. Another approach to solve this question is to use the unitary method for ratio.