Basic Inlet Outlet MCQ Quiz - Objective Question with Answer for Basic Inlet Outlet - Download Free PDF

Given:

Time taken to fill the tank by both pipes together = 45 minutes.

Pipe B fills the tank twice as fast as pipe A.

Formula Used:

Rate of filling = 1 / Time taken

Combined rate of filling = Rate of pipe A + Rate of pipe B

Calculation:

Let the time taken by pipe A alone to fill the tank be x minutes.

Then, the rate of filling of pipe A = 1/x

Since pipe B fills the tank twice as fast as pipe A, the time taken by pipe B alone to fill the tank will be x/2 minutes.

So, the rate of filling of pipe B = 2/x

The combined rate of filling of both pipes = 1/x + 2/x = 3/x

It is given that the combined rate of filling of both pipes = 1/45

Thus, we have:

3/x = 1/45

Solving for x:

⇒ x = 3 × 45

⇒ x = 135

Pipe A alone will take 135 minutes to fill the tank.

Shortcut Trick 

Given:

One pipe can fill a tank four times as fast as another pipe.

Both pipes together can fill the tank in 48 minutes.

Formula used:

If the faster pipe fills the tank in time t₁, then the slower pipe takes t₂ = 4 × t₁.

Their combined rate is:

(1/t₁) + (1/t₂) = 1/48

Calculations:

Step 1: Let the time taken by the faster pipe = t₁.

Time taken by the slower pipe = t₂ = 4 × t₁.

Step 2: Use the combined rate formula:

(1/t₁) + (1/(4 × t₁)) = 1/48

⇒ (4 + 1) / (4 × t₁) = 1/48

⇒ 5 / (4 × t₁) = 1/48

⇒ t₁ = (5 × 48) / 4

⇒ t₁ = 60 minutes

Step 3: Calculate the time taken by the slower pipe:

t₂ = 4 × t₁ = 4 × 60

⇒ t₂ = 240 minutes

∴ The slower pipe alone will be able to fill the tank in 240 minutes.

Given:

Filling time by tap 1 = 10 minutes.

Emptying time by tap 2 = 12 minutes.

Formula Used:

Net filling rate = Filling rate by tap 1 - Emptying rate by tap 2

Time to fill the tank = 1 / Net filling rate

Calculation:

Filling rate by tap 1 = 1/10 per minute

Emptying rate by tap 2 = 1/12 per minute

Net filling rate = 1/10 - 1/12

⇒ Net filling rate = (1)/(10) - (1)/(12)

⇒ Net filling rate = (6 - 5)/(60)

⇒ Net filling rate = 1/60 per minute

Time to fill the tank = 1 / (1/60) minutes

Time taken to fill the tank = 60 minutes = 1 hour.

The correct answer is option 4.

Given:

Pipe X can fill the tank in 14 hours.

Pipe Y can fill the tank in 21 hours.

Formula Used:

Combined rate of filling = (1/Time taken by X) + (1/Time taken by Y)

Calculation:

Rate of Pipe X = 1/14

Rate of Pipe Y = 1/21

Combined rate = (1/14) + (1/21)

Combined rate = (1/14) + (1/21)

Combined rate = (3/42) + (2/42)

Combined rate = (5/42)

Time taken to fill the tank = 1 / Combined rate

Time taken = (42/5)

Time taken = 8(2/5) hours

The empty tank will be filled in 8(2/5) hours.

Given:

An inlet pipe can fill a tank in 11 hours.

An outlet pipe can empty the tank in 15 hours.

We need to find the time taken to fill the tank if both pipes are opened simultaneously.

Concept used:

The effective rate of filling the tank is the difference between the rates of the inlet and outlet pipes. The rate of work is calculated as:

Inlet pipe rate = 1/11 (fraction of the tank filled per hour).

Outlet pipe rate = 1/15 (fraction of the tank emptied per hour).

Net rate = Inlet rate - Outlet rate.

Time taken to fill the tank = 1 / Net rate.

Calculation:

Calculate the net rate:

Net rate = (1/11) - (1/15)

Find the LCM of 11 and 15, which is 165:

Net rate = (15/165) - (11/165) = 4/165.

Step 2: Calculate the time taken to fill the tank:

Time = 1 / (4/165) = 165 / 4 = 41.25 hours.

The time taken to fill the empty tank is 41.25 hours or 41\(\frac{1}{4}\) hours.

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

Given:- 

An inlet pipe can fill an empty tank in 120 hours  

Formula Used:-

The total capacity of the tank (Work) = Efficiency × Time

Calculation:- 
 

	Time	Efficiency	Total work
inlet pipe	120	9	1080
outlet pipe	54	20

According to the question, 

8 inlet pipes and 3 outlet pipes are opened simultaneously 

⇒ work done 1 hours = 8 × 9 - 20 × 3 

⇒ 72 - 60 = 12

SO,

Time = 1080/12 = 90  

∴ The required answer is 90.

Given

A pipe can fill a tank in 30 hours.

Due to leakage at the bottom, it is filled in 50 hours.

Formula used:

Total work = man × efficiency

Calculation

Tank filled without leakage = 1/30

Tank filled with leakage = 1/50

Pipe empty the completely filled tank in one hour  = 1/30 – 1/50

= (5 - 3)/150

= 1/75

75 hours is the time taken to empty the completely filled tank.

Shortcut Tricktime taken to empty the completely filled tank = [(50) × 30] /(50 - 30)

= (1500)/(20)

= 75 hours

Given:

Each inlet pipe can fill an empty cistern in 84 hours while each drain pipe can empty the same cistern from a filled condition in 105 hours.

When the cistern is empty, 9 inlet pipes and 10 outlet pipes are simultaneously opened

Concept used:

Efficiency = (Total work / Total time taken)

Efficiency = work done in a single day 

Calculation:

Let total work is 420 units ( LCM of 84 and105 and)

The efficiency of 1 inlet pipe  = 420 /84

⇒ 5 units

The efficiency of 1 out let pipe= 420 / 105

⇒ 4 units

The efficiency of 9 inlet pipes = 9 × 5

⇒ 45 units

The efficiency of 10 outlet pipes = 10 × 4

⇒ 40 units

Total efficiency of  is (45 - 40) / = 5 units

The time will be   420 / 5  = 84 hrs

∴ The correct option is 1

Given: 

Pipe A can fill 50% of the tank in 6 hours and pipe B can completely fill the same tank in 18 hours

Concept used:

Efficiency = (Total work / Total time taken)

Efficiency = work done in a single day 

Calculation:

Pipe A can feel the complete tank in 6 × 2 = 12 hrs

Let total work is 36 units ( LCM of 12 and 18) 

The efficiency of pipe A is 36 /12 = 3units

The efficiency of pipe B is 36 /18 = 2units

The efficiency of pipe A + B is 2 + 3 = 5 units

The time will be , 36 /5 = 7.2 hrs

⇒ 7.2 × 60 = 432 minutes

∴ The correct option is 3

Given:

Pipes A can fill and B can fill a tank in 18 hours and 24 hours respectively..

Concept used:

Entire work = Work done hourly × Total time taken (in hours)

Calculation:

Total capacity = LCM (18, 24) = 72

Now,

Pipe A fill hourly by = 72 ÷ 18 = 4 units

Pipe B fills hourly by = 72 ÷ 24 = 3 units

The total tank will be filled in:

⇒ 72/(4 + 3)

⇒ 10(2/7) hours

They will take to fill the empty tank in 10(2/7) hours.

Concept used:

Efficiency = Total Work/ Total Time 

Calculation:

Let the total capacity of the tank = 72 units [LCM of 12, 18 and 36]

According to the question

Efficiency of Pipe A = 72/12 = 6

Efficiency of Pipe B = 72/18 = 4  

Efficiency of Pipe C = 72/36 = -2 (outlet pipe)  

Combined efficiency of (A + B + C) = 6 + 4 + (-2) = 8

So, Time taken by (A + B + C) to fill the tank = 72/8 = 9 minutes

The answer is 9 minutes.

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

Given:- 

An inlet pipe can fill an empty tank in 120 hours  

Formula Used:-

The total capacity of the tank (Work) = Efficiency × Time

Calculation:- 
 

	Time	Efficiency	Total work
inlet pipe	120	9	1080
outlet pipe	54	20

According to the question, 

8 inlet pipes and 3 outlet pipes are opened simultaneously 

⇒ work done 1 hours = 8 × 9 - 20 × 3 

⇒ 72 - 60 = 12

SO,

Time = 1080/12 = 90  

∴ The required answer is 90.

Given

A pipe can fill a tank in 30 hours.

Due to leakage at the bottom, it is filled in 50 hours.

Formula used:

Total work = man × efficiency

Calculation

Tank filled without leakage = 1/30

Tank filled with leakage = 1/50

Pipe empty the completely filled tank in one hour  = 1/30 – 1/50

= (5 - 3)/150

= 1/75

75 hours is the time taken to empty the completely filled tank.

Shortcut Tricktime taken to empty the completely filled tank = [(50) × 30] /(50 - 30)

= (1500)/(20)

= 75 hours