Pipes and Cisterns Questions and Answers
1) 13.5 litres capacity 12 Pots of water can be sufficient to fill a drum. How many 9 litres pots of water will be required to fill the above drum? ANS:- 18 Explanation:Capacity of the drum = (12 × 13.5) litres = 162 litres. Capacity of each pot = 9 litres. Total pots needed = 162/9 = 18 .
2) A Barrel can be filled by pipeA in 8 hours while pipeB can be empty the Barrel in 17 hours. If both the pipes start work at the same time, then find the time needed to fill the Barrel? Ans:- 15.11 hours Explanation:Net partion filled in 1 hour = [ 1/8 - 1/17] = 9/136 . The Barrel can be filled in 136/9 hrs = 15.11 hours.
3) A tap can fill a tank in 16 hours. After half the tank is filled, 3 more same capacity taps are opened. How much time needed to fill the tank? Ans:- 8 hrs 15 min Explanation:-
• Time taken by one tap to fill half the tank = 8 hrs. • Part filled by the four taps in 1 hour = 4 ×1/8 = 1/2 . Remaining part = [ 1 - 1/2 ] = 1/2 . • ∴ 1/2 : 1/2 : : 1 : A or A = [ 1/2 ×1 × 1/2 ] = 1/4 hrs i.e., 15 mins. • So, total time taken = 8 hrs 15 min.
4) A tap fill a pot in two hours because of a hole to the pot, it took 2 1/3 hours. Calculate the time needed for hole to emptied the pot completely? Ans:- 14 Explanation:-
• Job done by the hole in 1 hour = [ 1/2 - 3/7 ] = 1/14 . • So, hole can empty the pot in 14 hrs.
5) Mug P has 3times more capacity than Mug Q. It takes 60 turns for Mug P to fill the empty Drum. How many turns it will take for both the Mugs P and Q, having each turn together to fill the empty drum? Ans:- 45 Explanation:Let capacity of Mug P be n litres. Then, capacity of Mug Q = n/3 litres. Capacity of the drum = 60n litres. Required number of turns = [ 60n / ( n + n/3 ) ] = [ 60n × 3/4n ] = 45.
6)Pipe A can fill a tank in 5 hours and Pipe B can fill a tank in 6 hours. Pipe C can empty the tank in 12 hours. If all the three pipes are opened in the same time, then the tank will be filled in? Ans:- 3 9/17 hours Explanation:Net portion filled in 1 hour = [ 1/5 + 1/6 - 1/12 ] = 17/60 . So, The tank will be filled in 60/17 hrs i.e., 3 9/17 hours.
7) PipeA fill a tank 3times faster than PipeB. If two pipes can fill the tank in 36 minutes, then find the time needed for PipeB alone to fill the tank? Ans:- 144 minutes Explanation:Let us assume pipeB alone fill the tank in B minutes. Then, faster pipe will fill it in B/3 minutes. According to the question, 1/B + 3/B = 1/36 ↔ 4/B = 1/36 ↔ B = 144 min. • So, pipeB can fill the tank in 144 minutes.
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8) Pipe X can fill a tank in 50 hours, Pipe Y in 100 hours and pipe Z in 300 hours. If all the pipes are open, In how much time all 3 pipes fill the tank? Ans:- 30 Explanation:Part filled by (X + Y + Z) in 1 hour = [ 1/50 + 1/100 + 1/300 ] = 1/30 . ∴ All the three pipes together will fill the tank in 30 hours.
9) PipeA, PipeB and PipeC can fill a Cistern in 5 hours. The pipe C is twice as fast as pipe B and pipe B is twice as fast as pipe A. How much time will pipe A alone will take to fill the Cistern? Ans:- 35 hours Explanation:-
• Suppose pipe A alone takes A hours to fill the Cistern. • Then, pipes B and C will take A/2 and B/4 hours respectively to fill the tank. • So, 1/A + 2/A + 4/A = 1/5 ↔ 7/A = 1/5 A = 35 hrs.
10) Two pipes A and B can fill a barrel in 40 and 60 minutes respectively. Find the time to fill the Barrel if both the pipes are used? Ans:- 24 minutes Explanation:• Portion filled by pipeA in 1 min. = 1/40 ; • Portion filled by pipeB in 1 min = 1/60 . • Portion filled by pipes(A + B) in 1 min. = 1/40 + 1/60 = 1/24 . • pipes A and B can fill the tank in 24 minutes.