Three taps A, B and C can fill a tank in 12, 15 and 20 hours respectively. Tap A is open all the time and taps B and C are open for one hour each alternately. In how many hours will the tank be full?

Correct option is A

Given:

Tap A can fill the tank in 12 hours.
Tap B can fill the tank in 15 hours.
Tap C can fill the tank in 20 hours.
Tap A is open all the time, and taps B and C are open alternately for one hour each.
Find the total time required to fill the tank  

Solution:

A, B and C can fill a tank in 12, 15 and 20 hours respectively

LCM of 12, 15 and 20 = 60
Efficiency of A = $$\frac{60}{12} = 5 unit$$​​

Efficiency of B = $$\frac{60}{15 }= 4 unit$$ ​

Efficiency of C = $$\frac{60}{20} = 3 unit$$​​
Tank fill in 2 hours = 5+4+5+3 = 17 unit
Tank fill in 6 hours = 17× 3 = 51 unit
Remaining 60 – 51 = 9
Remaining will fill by next hours by tap A and B will fill = 5+4= 9 unit.
Therefore, time to fill the tank = 6 +1 = 7 hours.