Pipe and Cistern MCQ Quiz - Objective Question with Answer for Pipe and Cistern - Download Free PDF

Given:

Inlet pipe can fill three-fourths of the cistern in 24 minutes.

Outlet pipe can empty one-third of the cistern in 16 minutes.

Calculations:

Rate of the inlet pipe = (3/4) cistern / 24 minutes = 3 / (4 × 24) = 1 / 32 cistern per minute.

Rate of the outlet pipe = (1/3) cistern / 16 minutes = 1 / (3 × 16) = 1 / 48 cistern per minute.

When both pipes are opened together, the combined rate is:

Combined rate = Rate of inlet pipe - Rate of outlet pipe = 1/32 - 1/48

To subtract, find the LCM of 32 and 48, which is 96:

1/32 = 3/96, and 1/48 = 2/96, so combined rate = (3/96) - (2/96) = 1/96 cistern per minute.

Thus, the cistern will be filled in 96 minutes.

∴ The cistern will be completely filled in 96 minutes.

Given:

Pipe A can fill the tank in 816 minutes.

Pipe B can empty the tank in 1020 minutes.

Formula used:

Efficiency of Pipe A = 1 / 816 (since it fills the tank in 816 minutes)

Efficiency of Pipe B = -1 / 1020 (since it empties the tank in 1020 minutes)

Calculations:

When both pipes are opened together, the net efficiency is the sum of their efficiencies:

Net efficiency = (1 / 816) - (1 / 1020)

To calculate this, we first find the LCM of 816 and 1020, which is 8160:

Net efficiency = (10 / 8160) - (8 / 8160) = 2 / 8160

The time taken to fill the tank is the inverse of the net efficiency:

Time = 8160 / 2 = 4080 minutes

Convert this time into hours:

Time in hours = 4080 / 60 = 68 hours

∴ It will take 68 hours to fill the empty tank when both pipes are opened together.

Given:

Pipe A can fill the tank in 780 minutes

Pipe B can empty the tank in 975 minutes

Formula used:

Work = LCM of times taken

Efficiency = Work ÷ Time

Net work = Filling efficiency - Emptying efficiency

Time = Total work ÷ Net efficiency

Calculations:

LCM of 780 and 975 = 50700 units (Total work)

⇒ A’s 1 min work = 50700 ÷ 780 = 65 units

⇒ B’s 1 min work = 50700 ÷ 975 = 52 units

⇒ Net 1 min work = 65 - 52 = 13 units

⇒ Time = 50700 ÷ 13 = 3900 minutes

⇒ Convert to hours: 3900 ÷ 60 = 65 hours

∴ The tank will be filled in 65 hours.

Given:

Pipe A fills the tank in 105 minutes.

Pipe B fills the tank in 63 minutes.

Pipe C empties the tank in 42 minutes.

Formula used:

Time is taken to fill the tank = XYZ / (YZ + XZ -XY)

where X, Y, and Z are time taken by Pipe A, B, and C respectively.

Calculation:

Applying the above formula

Time taken to fill the tank = (105 × 63 × 42) / ( 63 × 42 + 105 × 42 - 105 × 63)

= 277830 / 441

= 630 minutes

∴ The correct answer is 630 minutes.

Given:

Pipe A can fill the tank in 165 minutes.

Pipe B can fill the tank in 99 minutes.

Pipe C can empty the tank in 66 minutes.

Formula used:

Efficiency of a pipe = 1 / Time taken by the pipe to fill/empty the tank

Let the total work be the LCM of 165, 99, and 66.

Calculations:

Let the capacity of the tank is = LCM of 165, 99, and 66 = 495

Efficiency of Pipe A = 495 / 165 = 3 (filling per minute)

Efficiency of Pipe B = 495 / 99 = 5 (filling per minute)

Efficiency of Pipe C = 495 / 66 = -7.5 (emptying per minute)

Net efficiency = 3 + 5 - 7.5 = 0.5 (filling per minute)

Time to fill the tank = Total work / Net efficiency = 495 / 0.5 = 990 minutes

∴ It will take 990 minutes to fill the tank when all three pipes are opened simultaneously.

Shortcut Trick

If both pipes are open, total efficiency = (A + B) = 5 + (-8) = -3 units

According to question,

Amount of water in the tank = (1/5) × 80 = 16 units

Time taken to empty the tank = work/efficiency = 16/((-3)) = 5.33 hours

Alternate Method

GIVEN :

Time by which pipe A can fill the tank = 16 hours

Time by which pipe B can empty the tank = 10 hours 

The cistern is (1/5)th full.

CONCEPT :

Total work = time × efficiency

CALCULATION :

Negative efficiency indicates pipe B is emptying the tank.

If both pipes are open, total efficiency = (A + B) = 5 + (-8) = -3 units

From the total efficiency it is clear that when both are opened, the tank is being emptied. 

Amount of water in the tank = (1/5) × 80 = 16 units

The water level will not rise as the total action is emptying when both are opened together.

Time taken to empty the tank = work/efficiency = 16/((-3)) = 5.33 hours

∴ Time taken to empty the tank is 5.33 hours.

Given:

First pipe can fill the cistern = 3 hours

Second pipe can fill the cistern = 4 hours

Third pipe can drain the cistern = 8 hours

Calculation:

Let the total amount of work in filling a cistern be 24 units. (LCM of 3, 4 and 8)

Work done by pipe 1 in 1 hour = 24/3 = 8 units.

Work done by pipe 2 in 1 hour = 24/4 = 6 units.

Work done by pipe 3 in 1 hour = 24/ (-8) = -3 units

Total work done in 1 hour = 8 + 6 – 3 = 11 units

The time required to complete 11/12^th of the work = 11/12 × 24/ 11 = 2 hours

∴ The correct answer is 2 hours.

Given: 

An inlet pipe can fill an empty tank in \(4\frac{1}{2}\) hours while an outlet pipe drains a completely filled tank in \(7\frac{1}{5}\) hours.

Concept used:

Efficiency = (Total work / Total time taken)

Efficiency = work done in a single day 

Calculation:Time taken by A = 9/2 hours

Please note that after 20 hours, the remaining capacity = 6 units

Now in the 21st hour, pipe A will work and fill the tank so no need to add time after that.

Time taken by pipe A to fill 6 units = 6/8 = 3/4 hours

So,

Shortcut Trick 

Given:

Pipes A can fill a tank with water in 30 minutes

Pipes B can fill a tank with water in 40 minutes

Pipe C can drain off 51 litres of water per minute

All the three pipes are opened together, the tank is filled in 90 minutes

Concept used:

LCM method used,

Calculation:

According to the question:

Lcm of (30, 40, 90) = 360

Efficiency of C = (12 + 9) - 4 = 17 l/min

Which is actually 51 litres/min,

⇒ 17 unit = 51lit

⇒ 360 unit = (51/17) × 360 = 1080 litres

∴ The capacity (in litres) of the tank is 1080 litres.

Calculation:

According to question

⇒ (M + N) × 20/3 = 4M + 9N

⇒ 20M + 20N = 12M + 27N

⇒ 8M = 7N

⇒ M/N = 7/8

To fill the complete tank by tap N = (4M + 9N)/efficiency of N

To fill the complete tank by tap N = (4 × 7 + 9 × 8)/8 = 100/8 = 25/2

Calculation:

Let capacity of cistern be x gallons

Pipe A fills cistern in 20 min

⇒ Cistern filled by pipe A in 1 hour = 3x

Pipe B fills cistern in 40 min

⇒ Cistern filled by pipe B in 1 hour = 60/40 = 1.5x

⇒ Water drained by waste pipe in 1 hour = 35 × 60 = 2100 gallons

If all three pipes are connected, Cistern fills in 1 hour

⇒ 3x + 1.5x - 2100 = x

⇒ 4.5x - x = 2100

⇒ 3.5x = 2100

⇒ x = 2100/3.5 = 600  

∴ The correct answer is 600 gallons

Alternate Method Let's denote the capacity of the cistern as C gallons. We then have:

The rate of the first pipe is C/20 gallons per minute.

The rate of the second pipe is C/40 gallons per minute.

The waste pipe drains at a rate of 35 gallons per minute.

When all three pipes are open, the cistern is filled in 60 minutes (1 hour), meaning the net rate is C/60 gallons per minute.

(C/20) + (C/40) - 35 = C/60

6C + 3C - 4200 = 2C

7C = 4200

C = 4200 / 7 = 600

So, the capacity of the cistern is 600 gallons.

Calculation:

Working together, pipes A and B can fill an empty tank in 10 hours,

⇒ 1/A + 1/B = 1/10

together they worked for 4 hours and then A continued, and work completed in 13 hrs,

It means A worked for 13 hrs.

⇒ (4/A + 4/B) + 9/A = 1

⇒ 4/10 + 9/A = 1

∴ A = 15 hrs

Alternate Method

Time is taken to fill the tank by A and B = 10 hrs = 100% of total work

A and B worked together for 4 hrs = 40% of total work

So,  6 hours of work remaining = 60% of total work

Work done by A alone = 13 - 4 = 9 hours

60% of work is done by A in 9 hours

100% of work = (9/60) × 100 = 15 hours

∴ The time taken by A to complete work is 15 hours.

Given:

Tap P can fill a tank = 20 hours

Tap Q can fill a tank = 25 hours

Tap R can fill a tank = 40 hours

Calculation:

Let the total work be LCM of 20, 25, and 40 = 200 units

⇒ Efficiency of tap P = 200/20 = 10 units

⇒ Efficiency of tap Q = 200/25 = 8 units

⇒ Efficiency of tap R = 200/40 = 5 units

Since the tap Q is kept open for 10 hours,

Work done by tap Q = 10 × 8 = 80 units

∵ Tap R is closed 9 hours before the tank overflows

⇒ Tap P alone worked for 9 hours.

⇒ Work done by tap P alone = 9 × 10 = 90 units

Remaining work = 200 - (80 + 90) = 30 units

The remaining work was done by tap P and tap R together

Time taken by tap P and Tap R to complete the remaining work = 30/(10 + 5) = 30/15 = 2 hours

∴ The total time to fill the tank is (10 + 9 + 2) 21 hours.

Given:

Time taken by A to fill tank = 6 hours

Time taken by B to fill tank = 8 hours

Time taken by A, B and, C together to fill the tank = 12 hours

Concept used:

Total work = time × efficiency 

Calculation:

Let the capacity of the tank ( work to be done) be 24x units (LCM of 6, 8, 12)

⇒ The efficiency of pipe A = 24x/6 = 4x units/day

⇒ Efficiency of pipe B = 24x/8 = 3x units/day

⇒ Efficiency of pipe (A + B + C) = 24x/12 = 2x units/day

⇒ Efficiency of pipe C = efficiency of (A + B = C) - efficiency of (A + B)

Efficiency of pipe C = 2x – (4x + 3x) = – 5x units/day

Negative efficiency implies that pipe C is emptying pipe.

⇒ Time taken by pipe C to empty the filled tank = 24x/5x

= 4.8 hours or 4 hrs 48 min

∴ The pipe C will empty the tank in 4 hrs 48 mins.

Given:

Pipe A and pipe B running together can fill a cistern in 6 minutes.

B takes 5 minutes more than A to fill it. 

Concept used:

Efficiency = (Total work / Total time taken)

Efficiency = work done in a single day 

Calculation:

Let Pipe A takes x minutes

So pipe B takes x+5 minutes

As per the question,

1/x + 1/(x+5) = 1/6

2x + 5 = x(x+5) 1/6

12x + 30 = x² + 5x

x2 - 7x - 30 = 0

(x+3)(x-10) = 0

So x = 10 

Time taken by B is 10 + 5 = 15 minutes

∴ The correct option is 4