Question

If the "X" tap is turned on, the water tank fills in 14 hours.
If the "Y" tap is turned on, the water tank fills in 20 hours.
If the "Z" tap is turned on, the water tank fills in 17 hours.
And
If the "P" tap is turned on, the water tank is empty within 8 hours.
How long will the tank fill if all four taps are turned on?

Not just the answer, the method has to be.​

Answer 1

Answer:

18.098 hours

Step-by-step explanation:

Let us assume that, the volume of the tank be "L" Liters.

So, it is given

14 hours required to fill L liters by X tap.

⇒1 hour required to fill $\frac{L}{14}$ liters by X tap.

Again, it is given

20 hours required to fill L liters by Y tap.

⇒1 hour required to fill $\frac{L}{20}$ liters by Y tap.

Again, it is given

17 hours required to fill L liters by Z tap.

⇒1 hour required to fill $\frac{L}{17}$ liters by Z tap.

Again, it is given

8 hours required to empty L liters by P tap.

⇒1 hour required to empty $\frac{L}{8}$ liters by P tap.

So, if all the taps are open then,

in 1 hour there will be filling of water by ($\frac{L}{14} +\frac{L}{20} +\frac{L}{17} -\frac{L}{8}$) liters.

⇒in 1 hour there will be filling of water by ($\frac{340+238+280-595}{4760}$) L liters.

⇒in 1 hour there will be filling of water by ($\frac{263}{4760}$) L liters.

Therefore, if all the four taps are open L liters of water will be filled in ($\frac{4760}{263}$) hours

= 18.098 hours. (Answer)