Examples(Set 1) - Pipes and Cistern

1. Pipes P and Q can fill a tank in 4 and 6 hours respectively. Pipe R can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in:
A. 3 and 1/2 hours
B. 3 hours
C. 4 hours
D. 7 hours
Answer: Option B

Explanation:
Pipes P can fill the tank in 4 hours.
part filled by pipe P in 1 hour = 1/ 4
Pipes Q can fill the tank in 6 hours.
part filled by pipe Q in 1 hour = 1/ 6
Pipe R can empty the tank in 12 hours.
part emptied by pipe R in 1 hour = 1/ 12
Net part filled by Pipes P,Q,R together in 1 hour
= 1/ 4 + 1/ 6 − 1/ 12
= 1/3
i.e., the tank can be filled in = 3 hours

2. A pump can fill a tank with water in 2 hours. Because of a leak, it took  $2\frac{2}{3}$ hours to fill the tank. The leak can drain all the water of the tank in
A. 9 hours
B. 8 hours
C. 10 hours
D. 6 hours

Answer: Option B

Explanation:
The pump can fill the tank in 2 hour Part of the tank filled by the pump in 1 hr = 1/ 2
Suppose the leak can drain all the water of the tank in x hours.
part of the tank emptied by the leak in 1 hr = 1/x.
Because of the leak, it took 2 and 2/3hours = 8/ 3 hours to fill the tank.
i.e., Part of the tank filled in 1 hour when the leak is there = 3/ 8
1/ 2 − 1/ x = 3/ 8
⇒ 1 /x = 1/ 2 − 3/ 8
= 1/ 8
⇒ x = 8

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3. Two pipes A and B can fill a cistern in $37\frac{1}{2}$ minutes and $45$ minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if pipe B is turned off after
A. 5 min	B. 9 min
C. 15 min	D. 10 min

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Answer: Option B

Explanation:
Part filled by pipe A in 1 minute $=\frac{2}{75}$
Part filled by pipe B in 1 minute $=\frac{1}{45}$

Suppose pipe B is closed after $x$ minutes. Then,
$\frac{2}{75}\times 30+\frac{1}{45}\times x=1\frac{4}{5}+\frac{x}{45}=1x=9$

4. Vrushabh's age is 125 % of what it was 10 years ago, but 250/3 % of what it will be after 10 years. What is his present age?
A. 40
B. 70
C. 50
D. 60

Answer: Option C

Explanation:
Let Vrushabh's age be V
V=125/100*(M-10)

M=50

5. Trisha is 24 years older than Megha. In two years, her age will be twice the age of Megha. What is the present age of megha?
A. 23 years
B. 22 years
C. 21 years
D. 20 years
Answer: Option B

Explanation:
Let Trisha's age be T
Let Megha's age be M
T=24+M
T+2=(M+2)*2

M=22