100+ Pipes and Cisterns Questions for Competitive Exams - 1

Question: 1

Pipes A and B can fill a tank in 20 hours and 30 hours respectively and pipe C can empty the full tank in 40 hours. If all the pipes are opened together, how much time will be needed to make the tank full?

(A) $$10{3}/{7}$$ hours

(B) $$12{4}/{5}$$ hours

(C) $$17{1}/{7}$$ hours

(D) $$19{1}/{4}$$ hours

Ans: C

Net part filled in 1 hour = $$({1}/{20} + {1}/{30} – {1}/{40})$$ = $${7}/{120}$$.

∴ The tank will be full in $${120}/{7}$$ i.e., $$17{1}/{7}$$ hours.

Question: 2

Two pipes A and B can fill a tank in 20 and 30 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?

(A) 12 min

(B) 14 min

(C) 15 min

(D) 17 min

Ans: A

Part filled by A in 1 min. = $${1}/{20}$$.

Part filled by B in 1 min. = $${1}/{30}$$.

Part filled by (A + B) in 1 min. = $$({1}/{20} + {1}/{30})$$ = $${1}/{12}$$.

∴ Both the pipes can fill the tank in 12 minutes.

Question: 3

Two pipes A and B can separately fill a cistern in 60 minutes and 75 minutes respectively. There is a third pipe in the bottom of the cistern to empty. If all the three pipes are simultaneously opened, then the cistern is full in 50 minutes. In how much time, the third pipe alone can empty the cistern?

(A) 90 min

(B) 100 min

(C) 110 min

(D) 120 min

Ans: B

Work done by the third pipe in 1 min.

=$${1}/{50} + ({1}/{60} + {1}/{75})$$ = $$({1}/{50} + {3}/{100})$$ = $${1}/{100}$$

[-ve signs means emptying]

The third pipe can empty the cistern in 100 min.

Question: 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?

(A) 3 hrs 15 min

(B) 3 hrs 30 min

(C) 3 hrs 45 min

(D) 4 hrs

Ans: C

Time taken by one tap to fill half the tank = 3 hrs.

Part filled by the four taps in one hour = $$(4 × {1}/{6})$$ = $${2}/{3}$$.

Remaining part = $${1}/{2}$$.

∴ $${2}/{3} : {1}/{2}$$ : : 1 : x or x = $$({1}/{2} × 1 × {3}/{2})$$ = $${3}/{4}$$ hrs i.e., 45 min.

So, total time taken = 3 hrs 45 min.

Question: 5

Two pipes A and B together can fill a cistern in 4 hours. Had they been opened separately, then B would have taken 6 hours more than A to fill the cistern. How much time will be taken by A to fill the cistern separately?

(A) 1 hr

(B) 2 hrs

(C) 4 hrs

(D) 6 hrs

Ans: D

Let the cistern be filled by pipe A alone in x hours.

Then, pipe B will fill it in (x + 6) hours.

∴ $${1}/{x} + {1}/{(x + 6)}$$ = $${1}/{4}$$

⇔ $${ x + 6 + x}/{x (x + 6)}$$ = $${1}/{4}$$

⇔ x2 - 2x – 24 = 0

⇔ (x – 6) (x + 4) = 0

⇔ x = 6.

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