Find in whichever condition/conditions filling of water tank is/are possible:
A. One tap filling the tank in 2 liter/minute.
B. One tap filling the tank in 15 liter/minute and one tap emptying the tank with speed 1 liter/minute.
C. Two taps filling the tank with uniform speed of 4 liter/minute and one tap emptying the tank with speed of 500 ml/sec.
D. One tap filling the tank in 2 liter/minute and one tap emptying the tank with speed 4 liter/minute.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Filled in case ‘A’ and ‘B’ Only
A tank fills only when water flows in faster than it flows out, so in each case the net rate is worked out in the same unit, litres per minute (500 ml/sec \(=0.5\times60=30\) litres a minute).
A. One tap filling the tank in 2 liter/minute. Filled. Nothing flows out, so the tank gains 2 litres a minute.
B. One tap filling the tank in 15 liter/minute and one tap emptying the tank with speed 1 liter/minute. Filled. The net gain is \(15-1=14\) litres a minute.
C. Two taps filling the tank with uniform speed of 4 liter/minute and one tap emptying the tank with speed of 500 ml/sec. Not filled. In: \(2\times4=8\) litres a minute; out: 30 litres a minute, so the tank loses 22 litres a minute.
D. One tap filling the tank in 2 liter/minute and one tap emptying the tank with speed 4 liter/minute. Not filled. The net change is \(2-4=-2\) litres a minute: it empties faster than it fills.