Three taps A,B and C can fill a tank in 12 minutes, 15 minutes and 20 minutes respectively. If tap A is opened all the time while tap B and C are opened for 1 minute each alternately such that tap B opened first, then the time taken to fill the tank is :
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 7 minutes
In one minute, A fills \( \frac{1}{12} \), B fills \( \frac{1}{15} \) and C fills \( \frac{1}{20} \) of the tank. Take 60 (the LCM) as the capacity: A fills 5 units, B 4 units and C 3 units per minute.
The taps work in 2-minute cycles: A + B in the first minute, A + C in the second.
\( \displaystyle \text{one cycle}=(5+4)+(5+3)=17\ \text{units in 2 minutes} \)
\( \displaystyle \text{after 3 cycles (6 minutes)}=51\ \text{units} \)
The remaining 60 − 51 = 9 units come in the 7th minute, when A and B are open together and fill 5 + 4 = 9 units.
So the tank is full in exactly 7 minutes.