Pipes And Cistern - Aptitude MCQ Questions and Solutions with Explanations

61

Pipe A can fill the tank in 8 hours and pipe B can fill it in 12 hours. If pipe A is opened at 7:00 am and pipe B is opened at 9:00 am, then at what time will the tank be full?

A) 12:00 PM B) 12:30 PM C) 11:48 PM D) 12:36 PM

Discuss

Answer & Solution

Answer: Option D

Solution:

A opened 2 hours early to B
In 2 hours A can do 3 × 2 = 6 unit work
Remaining work = 24 - 6 = 18
A + B can do it in $$ \to \frac{{18}}{5}$$
= $$3\frac{3}{5}{\text{ hrs}}$$
= 3 hrs 36 min
∴ Tank will be full in 9 am + 3 hrs 36 min = 12 : 36 pm

62

Pipes A, B and C can fill an empty tank in $$\frac{{30}}{7}$$ hours, if all the three pipes are opened simultaneously. A and B are filling pipes and C is an emptying pipe. Pipe A can fill tank in 15 hours and pipe C can empty it in 12 hours. In how long (in hours) can pipe B alone fill the empty tank?

A) 4 B) 6 C) 3 D) 5

Discuss

Answer & Solution

Answer: Option A

Solution:

A + B + C = 14
4 + B - 5 = 14
B = 15 unit
B = $$\frac{{60}}{{15}}$$ = 4 hours

63

Pipes A and B can fill a tank in 16 hours and 24 hours, respectively, whereas pipe C and empty the full tank is 40 hours. All three pipes are opened together, but pipe C is closed after 10 hours. After how many hours will the remaining part of the tank be filled?

A) 2 B) $$2\frac{1}{2}$$ C) 5 D) $$5\frac{1}{2}$$

Discuss

Answer & Solution

Answer: Option A

Solution:

All three pipe opened together in 10 hours = (15 + 10 - 6) × 10 = 190
Remaining work = 240 - 190 = 50
Remaining work done by A and B $$ = \frac{{50}}{{15 + 10}} = 2$$

64

There are 3 taps, A, B and C, in a tank. These can fill the tank in 10 h, 20 h and 25 h, respectively. At first, all three taps are opened simultaneously. After 2 h, tap C is closed and tap A and B keep running. After 4 h, tap B is also closed. The remaining tank is filled by tap A alone. Find the percentage of work done by tap A itself.

A) 75% B) 52% C) 72% D) 32%

Discuss

Answer & Solution

Answer: Option C

Solution:

C's work done in 2 hour = 4 × 2 = 8
B's work done in 4 hour = 5 × 4 = 20
A's share of work = 100 - 28 = 72

65

Pipes A, B and C can fill a tank in 30h, 40h and 60h respectively. Pipes A, B and C are opened at 7 a.m., 8 a.m., and 10 a.m., respectively on the same day. When will the tank be full?

A) 10:00 pm B) 9:20 pm C) 10:20 pm D) 9:40 pm

Discuss

Answer & Solution

Answer: Option B

Solution:

Till 10 am
3A + 2B + (A + B + C)t = 120
3 × 4 + 2 × 3 + (4 + 3 + 2)t = 120
9t = 120 - 18
t = $$\frac{{102}}{9}$$
t = $$11\frac{1}{3}$$
t = 11 hr 20 min
10 am + 11:20 = 21:20 = 9:20 pm

66

Pipes A and B can fill a tank in one hour and two hours respectively while pipe C can empty the filled up tank in one hour and fifteen minutes. A and C are turned on together at 9 a.m. After 2 hours. Only A is closed and B is turned on. When will the tank be emptied?

A) 12:10 p.m. B) 11:30 a.m. C) 10:30 a.m. D) 12:20 p.m.

Discuss

Answer & Solution

Answer: Option D

Solution:

At 11 am, A is closed, now (B + C) will work together
B + C = 5 - 8 = -3
The time was taken to fill 4 unit
$$t = \frac{4}{3} = 1\frac{1}{3} = 1\,{\text{hr}}\,20\,\min $$
Pipes and Cistern mcq question image

67

Two pipes A and B can fill a cistern in $$12\frac{1}{2}$$ hours and 25 hours, respectively. The pipes are opened simultaneously and it is found that due to a leakage in the bottom, it took 1 hour 40 minutes more to fill the cistern. When the cistern is full, in how much time will the leak empty the cistern?

A) 48 hours B) 45 hours C) 42 hours D) 50 hours

Discuss

Answer & Solution

Answer: Option D

Solution:

Given:
A can fill the cistern 12.5 hr
B can fill the cistern 25 hr
Formula Used:
Total work = Efficiency × Time
Calculation:
Let the capacity of the cistern be 25 units (LCM of 12.5 and 25)
⇒ Efficiency of A = $$\frac{{25}}{{12.5}}$$ = 2 units/hr
⇒ Efficiency of B = $$\frac{{25}}{{25}}$$ = 1 units/hr
⇒ Combined efficiency of A and B = 2 + 1 = 3 units/hr
Time taken by A and B to fill the cistern without leakage ⇒ $$\frac{{25}}{3}$$ = $$8\frac{1}{3}$$ hr = 8 hr 20 min
Time taken by A and B to fill the cistern with leakage ⇒ 8 hr 20 min + 1 hr 40 min = 10 hr
The combined efficiency of A and B with leakage ⇒ $$\frac{{25}}{{10}}$$ = 2.5 units/hr
⇒ Efficiency of leakage = 3 - 2.5 = 0.5 units/hr
Time required by the leak to empty the full cistern ⇒ $$\frac{{25}}{{0.5}}$$ = 50 hr
∴ The leak can empty the full cistern in 50 hours.