1. Two pipes can fill a tank in 10 hours and 12 hours respectivley while a third pipe empties the full tank in 20 hours . If all the three pipes operates simultaneously, in how much time will the tank be filled ?
(a) 10 hrs (b) 20 hrs © 7 hrs 30 mins (d) none of the above
Explanation
Net part filed in 1 hour = (1/10 + 1/12 -1/20)
= 8/60 = 2/25
The tank will be full in 15/2 hrs = 7 hrs 30 mins
2.An electric pump can fill a tank in 3 hours.Because of a leak in the tank. It took 3 1/2 hour to fill the tank.If the tank is full, how much time will it take to empty it ?
(a) 6 hrs (b) 10hrs © 20 hrs (d) 21 hrs
Explanation
Work done by the leak in 1 hour = [1/3- 1/7/2] = (1/3- 2/7)
= 1/21
The leak will empty the tank in 21 hours
3.Two pipe A and B can fill a cistern in 37 1/2 minutes and 45 minutes respectivley .Both pipes are opened . The cistern will be filled in just half an hour, if the pipe B is turned off after
(A) 8 (B) 9 © 10 (D) 6
Explanation
Let B be turned off after x minutes .Then
Part filled by (A + B) in x min = + part filled By A in ( 30 — x) min = 1
x(2/75 + 1/45) + (30 — X) 2 / 75 = 1
11X / 225 + (60–2x) / 75 = 1
11 x + 180 -6x = 225
x = 9
4. A tap can fill a tank in 6 hours. After half the tank is filled, three more similar taps are opened. what is the total time taken to fill the tank completely?
Explanation
Time taken by one tap to fill half the tank =3 hrs
Part filled by the four taps in 1 hour = (4 * 1/6) = 2/3
Remaining part = (1–1/2) = 1/2
therefore 2/3:1/2 : :1:x = > x = (1/2 *1 * 3/2)
= 3/4 hrs
= 45 mins
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