Exercise : Pipe & Cistern - General Questions
✔ Pipe & Cistern -
General Questions
11.
Twelve taps are fitted to a tank. Some are fill pipes and others are outlet pipes. Each fill pipe can fill in 6 hrs and each outlet can empty in 12 hrs. If all are open, the tank fills in 4 hrs. How many fill pipes are there?
View Answer
Answer: Option A
Explanation:
Explanation:
Let \(x\) be fill pipes. \(x(1/6) - (12-x)(1/12) = 1/4 \implies 2x - 12 + x = 3 \implies 3x = 15 \implies x = 5\) fill pipes.
12.
A pipe can fill a tank in 15 mins and another in 10 mins. A third pipe empties it at 5 gallons per minute. If all three work, it fills in 30 mins. What is the capacity of the tank?
View Answer
Answer: Option A
Explanation:
Explanation:
\(1/15 + 1/10 - 1/C = 1/30 \implies 1/C = 1/15 + 1/10 - 1/30 = 4/30 = 2/15\). Outlet empties tank in 7.5 mins. Capacity = \(7.5 \times 5 = 37.5\) gallons.
13.
Pipe A fills in 20 hrs, B in 30 hrs. There is a leak which empties \(1/4\) of the total water filled by A and B. How long will it take to fill the tank?
View Answer
Answer: Option A
Explanation:
Explanation:
Combined rate = \(1/12\). Effective rate = \(3/4\) of \(1/12 = 1/16\). Time = 16 hours.
14.
Two pipes A and B can fill a tank in 24 and 32 mins. If both are opened together, after how much time should B be closed so that the tank is full in 18 minutes?
View Answer
Answer: Option A
Explanation:
Explanation:
A works for 18 mins. Work by A = \(18/24 = 3/4\). Remaining \(1/4\) done by B. Time for B = \((1/4) \times 32 = 8\) minutes.
15.
A cistern has three pipes A, B, and C. A and B can fill it in 3 and 4 hours respectively while C can empty it in 1 hour. If pipes are opened at 3, 4, and 5 PM, when is it empty?
View Answer
Answer: Option A
Explanation:
Explanation:
At 5 PM: A worked 2 hrs (2/3 full), B worked 1 hr (1/4 full). Total = 11/12 full. Net rate after 5 PM = \(1/3 + 1/4 - 1 = -5/12\). Time to empty = \((11/12) / (5/12) = 2.2\) hours = 2 hrs 12 mins. 5 PM + 2:12 = 7:12 PM.
16.
Three pipes A, B, and C fill a tank in 6 hours. After 2 hours, C is closed and A and B fill the remaining part in 7 hours. How long for C alone?
View Answer
Answer: Option A
Explanation:
Explanation:
2 hours work = \(2/6 = 1/3\). Remaining = \(2/3\). \((A+B)\) rate = \((2/3) / 7 = 2/21\). C rate = \(1/6 - 2/21 = (7-4)/42 = 3/42 = 1/14\). Time = 14 hours.
17.
A pipe of diameter 'd' can drain a tank in 40 mins. How long will a pipe of diameter '2d' take?
View Answer
Answer: Option A
Explanation:
Explanation:
Rate \(\propto\) Area \(\propto d^2\). Diameter doubles, rate becomes 4x. Time = \(40 / 4 = 10\) minutes.
18.
Two pipes A and B can fill a tank in 15 and 20 hours. Pipe C empties it in 25 hours. All pipes are opened. After 10 hours, C is closed. How much more time to fill?
View Answer
Answer: Option A
Explanation:
Explanation:
Rate = \(1/15 + 1/20 - 1/25 = 23/300\). 10 hours work = \(230/300 = 23/30\). Rem = \(7/30\). \((A+B)\) rate = \(35/300 = 7/60\). Time = \((7/30) / (7/60) = 2\) hours.
19.
A tank is filled by three pipes whose diameters are 1 cm, 2 cm, and 3 cm. The largest pipe alone fills it in 22 mins. The amount of water is proportional to the square of diameter. Time for all three?
View Answer
Answer: Option A
Explanation:
Explanation:
Rates: \(1^2, 2^2, 3^2 = 1, 4, 9\). Total work = \(9 \times 22 = 198\) units. Combined rate = \(1+4+9 = 14\). Time = \(198 / 14 = 14\frac{1}{7}\) minutes.
20.
A tank is \(2/5\) full. Pipe A fills in 10 mins, B empties in 6 mins. If both are opened, how long will it take to empty the tank?
View Answer
Answer: Option A
Explanation:
Explanation:
Net rate = \(1/10 - 1/6 = -2/30 = -1/15\) (Emptying). Time to empty \(2/5\) volume = \((2/5) \times 15 = 6\) minutes.