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Pipes & Cisterns

মোট প্রশ্ন৪০৮এই পাতা৭প্রতি পাতা১০০
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উত্তরিতবর্তমানপুনরায় দেখুনঅসম্পূর্ণ

Pipes & Cisterns

PrepBank · পাতা ৫ / ৫ · ৪০১–৪০৭ / ৪০৮

৪০১.
I have two inlet pipes in my tank. Pipe P is diametrically bigger than Q and can fill a tank alone in 22 hours while Pipe Q takes 11 hours longer than Pipe P to fill the tank. If I open both the inlet pipes together, how long will they take to fill the tank?
  1. ক
    ক) 19/22 hours
  2. খ
    খ) 1(1/11) hours
  3. গ
    গ) 13(1/5) hours
  4. ঘ
    ঘ) 18 hours
ব্যাখ্যা

Tank filled or work done by P in 1 hour = 1/22
Tank filled or work done by Q in 1 hour (Q takes 11 hrs more than P) = 1/33

Tank filled or work done by both pipes in 1 hour = 1/22 + 1/33 = 5/66
So the entire tank is full in = 66/5 = 13(1/5) hours.

৪০২.
Two pipes A and B can fill a tank in 20 and 30 hours respectively. If both the pipes are used together, then how long will it take to fill the tank?
  1. ক
    12 hours
  2. খ
    13 hours
  3. গ
    15 hours
  4. ঘ
    18 hours
ব্যাখ্যা
Question: Two pipes A and B can fill a tank in 20 and 30 hours respectively. If both the pipes are used together, then how long will it take to fill the tank?

Solution: 
Part filled by A in 1 hour = 1/20

Part filled by B in 1 hour = 1/30

Part filled by (A + B) in 1 hour
= 1/20 + 1/30 = 5/60 = 1/12

∴ Both pipes can fill the tank in 12 hours
৪০৩.
Two pipes A and B can fill a tank in 24 and 32 min, respectively. If both the pipes are opened together, after how much time pipe B should be closed so that the tank is full in 9 min?
  1. ক
    ক) 40 min
  2. খ
    খ) 30 min
  3. গ
    গ) 10 min
  4. ঘ
    ঘ) 25 min
  5. ঙ
    ঙ) 20 min
ব্যাখ্যা

Let, the total capacity of the tank be 96 units (LCM of 24 & 32).

A fills = 96/24 = 4 units / minute.
B fills = 96/32 = 3 units / minute

Let the time for which B is opened is x minutes.
According to the question, 
4 × 9 + 3 × x = 96
3x = 96 - 36
3x = 60
x = 20 minutes.
The pipe B should be closed after 20 minutes

৪০৪.
Three taps A, B, and C can fill a tank in 12,15, and 20 hours respectively. If A is open all the time and B, and C are open for one hour each alternatively, the tank will be full in:
  1. ক
    ক) 4 hrs
  2. খ
    খ) 5 hrs
  3. গ
    গ) 6 hrs
  4. ঘ
    ঘ) 7 hrs
ব্যাখ্যা
Question: Three taps A, B, and C can fill a tank in 12,15, and 20 hours respectively. If A is open all the time and B, and C are open for one hour each alternatively, the tank will be full in:

Solution:
A ১ ঘণ্টায় করে ১/১২ অংশ 
B ১ ঘণ্টায় পূর্ণ করে ১/১৫ অংশ 
C ১ ঘণ্টায় পূর্ণ করে ১/২০ অংশ 

A ও B ১ ঘন্টায় করে (১/১২) + (১/১৫) অংশ 
= ৩/২০ অংশ 

A ও C অংশ ১ ঘণ্টায় করে (১/১২) + (১/২০) অংশ 
= ২/১৫ অংশ 

২ ঘণ্টায় পূর্ণ হয় = (৩/২০) + (২/১৫)
= ১৭/৬০ অংশ 
৪ ঘণ্টায় পূর্ণ হয় (২ × ১৭)/৬০ অংশ 
= ৩৪/৬০ অংশ 
৬ ঘণ্টায় পূর্ণ হয় (৩৪/৬০) + (১৭/৬০)
= (৩৪ + ১৭)/৬০ অংশ 
= ৫১/৬০ অংশ 

বাকি থাকে (১ - ৫১/৬০)
= ৯/৬০ অংশ 
= ৩/২০ অংশ 

A ও B ১ ঘন্টায় করে (১/১২) + (১/১৫) অংশ 
= ৩/২০ অংশ 

∴ মোট সময় লাগবে = ৬ + ১ ঘণ্টা 
= ৭ ঘণ্টা
৪০৫.
A pipe can fill a tank in 6 hours. Because of a leak, it took 1 hour more to fill the tank. The leak can drain all the water from the tank in -
  1. ক
    ক) 7 hours
  2. খ
    খ) 14 hours
  3. গ
    গ) 36 hours
  4. ঘ
    ঘ) 42 hours
ব্যাখ্যা
Question: A pipe can fill a tank in 6 hours. Because of a leak, it took 1 hour more to fill the tank. The leak can drain all the water from the tank in -

Solution:
Because of the leak, it took 6 + 1 = 7 hours to fill the tank

Work done by pipe + leak in 1 hour = 1/7 part
Work done by pipe in 1 hour = 1/6 part

So, Work done by the leak in 1 hour = 1/6 - 1/7 part
= 1/42 part

∴ the leak will empty the tank in 42 hours
৪০৬.
Two taps can fill a cistern in 30 and 40 minutes respectively. If both the taps are opened simultaneously then the approximate time taken to fill the cistern is -
  1. ক
    ক) 17(1/7) minutes
  2. খ
    খ) 12(1/5) minutes
  3. গ
    গ) 19(1/2) minutes
  4. ঘ
    ঘ) 21(1/4) minutes
ব্যাখ্যা

We know that,
Two pipes A and B can fill (or empty) a tank in X and Y minutes respectively, while working alone.
If both the pipes are opened together,
then the time taken to fill (or empty) the cistern is given by XY/(X+Y) minutes.
Here,
X = 30 minutes and Y = 40 minutes
Therefore,
the required time = (30 x 40)/(30 + 40)
= 1200/70
= 120/7
= 17(1/7) minutes.
Hence the answer is 17(1/7) minutes.

৪০৭.
Three pipes A, B and C were opened to fill a cistern. Working alone, A, B and C require 12, 15 and 20 minutes respectively. Another pipe D, which is a waste pipe, can empty the filled tank in 30 minutes working alone. What is the total time (in minutes) taken to fill the cistern if all the pipes are simultaneously opened?
  1. ক
    5 minutes
  2. খ
    6 minutes
  3. গ
    7 minutes
  4. ঘ
    8 minutes
  5. ঙ
    None of these
ব্যাখ্যা
Question: Three pipes A, B and C were opened to fill a cistern. Working alone, A, B and C require 12, 15 and 20 minutes respectively. Another pipe D, which is a waste pipe, can empty the filled tank in 30 minutes working alone. What is the total time (in minutes) taken to fill the cistern if all the pipes are simultaneously opened?

Solution:
Let the capacity of the cistern be LCM(12, 15, 20, 30) = 60 units.
Efficiency of pipe A = 60 / 12 = 5 units / minute
Efficiency of pipe B = 60 / 15 = 4 units / minute
Efficiency of pipe C = 60 / 20 = 3 units / minute
Efficiency of pipe D = 60 / 30 = 2 units / minute

Combined efficiency of pipe A, pipe B, pipe C and pipe D = 10 units/minute  
Therefore, time required to fill the cistern if all the pipes are opened simultaneously = 60/10 = 6 minutes