1. A tank has two pipes. The first pipe can fill it in 24 minutes and the second can empty it in 32 minutes. If the two pipes be opened together at a time then find the time in which tank will be filled ?
Sol:
∴ time in which tank will be full = \(\frac{{96}}{{4 – 3}}\) = 96 minutes Answer
2. Pipe A can fill the tank in 5 hours and pipe B can fill the tank in 8 hours and a third pipe C can empty the tank in 4 hours. If all the pipes are opened together then after 10 hours what portion of the tank will be filled ?
Sol:
\({(A + B + C)_{eff}}\) = 8 + 5 – 10 = 3
tank filled in 10 hours = 3 × 10 = 30
∴ required portion = \(\frac{{30}}{{40}}\) = \(\frac{3}{4}\) Answer
3. A tank is fitted with two taps. The first tap can fill tank completely in 24 minutes and the second tap can empty the full tank in 32 minutes. If both the taps are opened alternately for one minute, then in how many hours the empty tank will be filled completely.
Sol:
Remaining 96 – 92 = 4 unit of tank will be filled in next one minute by pipe A
∴ total time to fill = 184 + 1 = 185 minutes = 3h5m Answer
4. Two pipes A and B can fill a cistern in 45 minutes and 60 minutes respectively. If both the pipes are opened together, then after how much time should B be closed so that the tank is full in 30 minutes ?
Sol:
pipe A remains open for full time i.e. 30 minutes
in 30 minutes it will fill 4 × 30 = 120 unit tank
Remaining 180 – 120 = 60 units will be filled by pipe B in \(\frac{{60}}{3}\) = 20 minutes
∴ pipe B is closed in 20 minutes Answer
5. Pipe A can fill an empty tank in 4 hours and pipe B in 16 hours. If both the pipes open alternately for 2 hours. In how much time B will take to fill the remaining tank ?
Sol:
tank filled by A & B in two hours alternately = 4 + 1 = 5 units
Remaining capacity of tank = 16 – 5 = 11 units
∴ time taken by B to fill the remaining part = \(\frac{{11}}{1}\) = 11 hours Answer
6. A tap drops at a rate of one drop/sec. 240 drops makes 100 ml. Find the number of liters wasted in 1 year. A year has 365 days.
Sol:
240 drop ⟶ 100 ml
2400 drop ⟶ 1 litre
Required number = \(\frac{{365 \times 24 \times 60 \times 60}}{{2400}}\) = 13140 litre Answer
7. Two pipes can separately fill a tank in 10 hours and 15 hours respectively. Both the pipes are opened to fill the tank but when the tank is \({\frac{1}{6}^{th}}\) full a leak develops in the tank through which \({\frac{1}{6}^{th}}\) of the water supplied by both the pipes leak out. what is the total time taken to fill the tank ?
Sol:
Remaining capacity = 30 – 5 = 25 unit
efficiency of leak = \( – \frac{1}{6}(3 + 2) = – \frac{5}{6}\)
Now both the pipes and leak are working to fill the remaining capacity of the tank ⟶ time taken = \(\frac{{25}}{{3 + 2 – \frac{5}{6}}}\) = 6 hours
∴ total time to fill the tank = 1 + 6 = 7 hours Answer
8. A pipe can empty a tank in 8 minutes and another pipe can empty it in 16 minutes. If both the pipes are opened simultaneously, find the time in which a full tank is emptied.
Sol:
time taken to empty the tank = \(\frac{{16}}{{(2 + 1)}}\) = \(\frac{{16}}{3}\) minutes Answer
9. Tap A can fill a water tank in 10 minutes, tab B can fill the same tank in 20 minutes and tap C can empty in 15 minutes. In how much time they completely filled up or emptied the tank ?
Sol:
\({(A + B + C)_{eff}}\) = 6 + 3 – 4 = 5
∴ tank will be filled in \(\frac{{60}}{5}\) = 12 minutes Answer
10. Three pipes A, B and C are connected to a tank. A & B together can fill the tank in 10 minutes, B & C together in 20 minutes and C & A together in 15 minutes. In how much time will each pipe fill the tank ?
Sol:
\(2{(A + B + C)_{eff}}\) = 6 + 3 + 4 = 13
∴ \({(A + B + C)_{eff}}\) = 6.5
∴ \({A_{eff}}\) = 6.5 – 3
\({B_{eff}}\) = 6.5 – 4 = 2.5
\({C_{eff}}\) = 6.5 – 6 = 0.5
∴ Time taken by A = \(\frac{{60}}{{3.5}}\) = \(\frac{{120}}{7}\) minutes
Time taken by B = \(\frac{{60}}{{2.5}}\) = \(\frac{{120}}{5}\) = 24 minutes
Time taken by C = \(\frac{{60}}{{0.5}}\) = 120 minutes Answer