Question

The volume of a pool is 4000 liters.
Ria's pipe takes 8 hours, while Pia's pipe takes 5 hours to fill the pool completely.

If both Ria and Pia start filling the pool, how much time will they take to fill the pool completely?

• A. $3\frac{1}{13}\text{hours}$
• B. $3\frac{2}{13}\text{hours}$
• C. $3\frac{13}{40}\text{hours}$
• D. $3\frac{1}{40}\text{hours}$

Answer 1

The correct option is A $3\frac{1}{13}\text{hours}$

Time taken by Ria to fill the pool = 8 hours
Time taken by Pia to fill the pool = 5 hours

The volume of the pool = 4000 liters

Liters of water filled in 1 hour

$=\frac{Totalvolumeofthepool}{Timetakentofillthepool}$

$\text{So, Ria filled}=\frac{4000}{8}=500\text{liters in 1 hour}$

$\text{So, Pia filled}=\frac{4000}{5}=800\text{liters in 1 hour}$

∴ Total liters of water filled in 1 hour by both of them = 500 + 800 = 1300 liters

So, the total time taken to fill the pool completely will be
$=\frac{Totalvolumeofthepool}{Litersofwaterfilledin1hour}$

$=\frac{4000}{1300}=3\frac{1}{13}\text{hours}$


Thus, the total time taken to fill the $\text{pool completely is}3\frac{1}{13}\text{hours.}$