A pool has 3 taps. The first tap takes 4 days, the second tap takes 2 days and the third tap takes only 12 h to fill the pool. How long will it take to fill the pool using all the three taps?

Correct option is C

Given:

Tap 1 fills the pool in 4 days,

Tap 2 fills the pool in 2 days,

Tap 3 fills the pool in 0.5 days

Formula Used:

Rate to fill tank = $$\frac{\text{Capacity}}{\text{Time}}$$​​

Solution:

Let the capacity of the pool is 4 units,

Tap 1 rate = $$\frac{4}{4}$$​ = 1 unit/day

Tap 2 rate = $$\frac{4}{2}$$​ = 2 units/day

Tap 3 rate = $$\frac{4}{0.5}$$​ = 8 units/day.

Now, the combined rate is the sum of the individual rates:

Total rate = 1 + 2 + 8 = 11 units/day.

The time to fill the pool when all three taps are open is:

Time = $$\frac{4}{11} days=\frac{4\times24}{11}hours$$​​

=$$\frac{96}{11}hours = 8\frac{8}{11}hours$$​​

Thus, it will take $$8\frac{8}{11}$$​hours to fill the pool with all three taps open.