Directions: Each of the questions given below is followed by series of options among which you have to choose the best one. You can also review your choices by clicking into answer section.
16. Pipes P and Q can empty a tank in 1 hr and 1.5 hrs respectively. Pipes R and S can fill a tank in 2 hrs and 2.5 hrs respectively. The tank is filled to its capacity of 15 liters and all four pipes are opened simultaneously. How much water remains in the tank after an hour?
A. 7 liters
B. 5 liters
C. 3.5 liters
D. 2.5 liters
Answer
Explanation:
Part of tank emptied by P in an hour = 1
Part of tank emptied by Q in an hour = 1/1.5 = 2/3
Part of tank filled by R in an hour = ½
Part of tank filled by S in an hour = 1/2.5 = 2/5
Part of tank emptied in an hour = (1+(2/3)) – ( ½ +(2/5)) = 23/30
Water remaining in the tank = 15*7/30 = 3.5 liters
17. A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?
A. 20 hours
B. 25 hours
C. 35 hours
D. Cannot be determined
Answer
Explanation:
Suppose pipe A alone takes x hours to fill the tank.
Then, pipes B and C will take x/2 and x/4 hours respectively to fill the tank.
1/x + 2/x + 4/x = 1/5
or, 7/x = 1/5
So, x = 35 hrs.
18. Three pipes, A, B, & C are attached to a tank. A & B can fill it in 20 & 30 minutes respectively while C can empty it in 15 minutes. If A, B & C are kept open successively for 1 minute each, how soon will the tank be filled?
A. 180 minutes
B. 167 minutes
C. 200 minutes
D. 178 minutes
Answer
Explanation:
No explanation
19. A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 liters a minute. When the tank is full, the inlet is opened and due to the leak, the tank is empty in 24 hours. How many liters does the cistern hold?
A. 4010 liter
B. 2220 liter
C. 1920 liter
D. 2020 liter
Answer
Explanation:
Part emptied by the leak in 1 hour = 1/6
Net part emptied by the leak and the inlet pipe in 1 hour = 1/24
Part filled by the inlet pipe in 1 hour = (1/6)− (1/24) = 1/8
i.e., inlet pipe fills the tank in 8 hours = (8 × 60) minutes = 480 minutes
Given that the inlet pipe fills water at the rate of 4 liters a minute
Hence, water filled in 480 minutes = 480 × 4 = 1920 liter
i.e. the cistern can hold 1920 liter
20. Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 7 hours. The number of hours taken by C alone to fill the tank is:
A. 10
B. 12
C. 14
D. 16
Answer
Explanation:
Part filled in 2 hours =2/6 = 1/3
Remaining part = 1/3 – 1 = 2/3 .
(A + B)'s 7 hour's work = 2/3
(A + B)'s 1 hour's work = 2/21
C's 1 hour's work
= { (A + B + C)'s 1 hour's work} – { (A + B)'s 1 hour's work }
=1/6 – 2/21
= 1/14
So, C alone can fill the tank in 14 hours.
22. A booster pump can be used for filling as well as for emptying a tank. The capacity of the tank is 2400 m3. The emptying of the tank is 10 m3 per minute higher than its filling capacity and the pump needs 8 minutes lesser to empty the tank than it needs to fill it. What is the filling capacity of the pump?
A. 20 m3 / min.
B. 40 m3 / min.
C. 50 m3 / min.
D. 60 m3 / min.
Answer
Explanation:
Let the filling capacity of the pump = x m3 / min.
Then the emptying capacity of the pump = (x + 10) m3 / min.
Time required for filling the tank = 2400x minutes
Time required for emptying the tank = 2400x/(x+10) minutes
Pump needs 8 minutes lesser to empty the tank than it needs to fill it
⇒2400x−2400x/(x+10)=8x
⇒300x−300x/(x+10)=1x
⇒300(x+10)−300x=x(x+10)
⇒3000=x2+10x
⇒x2+10x−3000=0
⇒(x+60)(x−50)= 0
⇒x = 50 or, -60
Since x cannot be negative, x=50
i.e. filling capacity of the pump = 50 m3 / min.
23. Pipe A and Pipe B can fill a tank in 20 minutes and 10 minutes respectively. Pipe C can empty the tank in 15 minutes. If the three pipes are opened simultaneously, find the time taken to fill the tank.
A. 12
B. 15
C. 20
D. 18
Answer
Explanation:
No explanation
24. Two pipes A and B can fill a cistern in 37 minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the B is turned off after:
A. 5 min.
B. 9 min.
C. 10 min.
D. 15 min.
Answer
Explanation:
Let B be turned off after x minutes. Then,
Part filled by (A + B) in x min. + Part filled by A in (30 -x) min. = 1/x.
(2/75)+(1/45) + (30 – x)*(2/75) = 1
or, (11x/225)+(60 -2x)/75 = 1
or, 11x + 180 – 6x = 225.
Hence, x = 9.
25. To fill a cistern, pipes A, B and C take 20 minutes, 15 minutes and 12 minutes respectively. The time in minutes that the three pipes together will take to fill the cistern, is :
A. 5
B. 12
C. 10
D. 15 2/3
Answer
Explanation:
Part filled by (A +B+ C) in 1 min.
= (1/20) + ( 1/15) + (1/12)
= 12/60 = 1/5
All the three pipes together will fill the tank in 5 min.
26. There are 10 pipes connected to a tank, some are inlet pipes and the others are outlets. Each of the inlet pipes can fill the tank in 6 hours and each of the outlet pipes can drain the entire tank in 8 hours. If all the pipes are opened when the tank is full, the tank is drained in half a day. How many of them are outlet pipes?
A. 4
B. 5
C. 6
D. 7
Answer
Explanation:
Let there be x inlet pipes and (10-x) outlet pipes
Part of tank filled by an inlet pipe in an hour = 1/6
Part of tank drained by an outlet pipe in an hour = 1/8
If all the pipes are opened, the tank is drained in half a day (12 hours).
Part of tank drained in an hour when all are open = 1/12
Part of tank drained by (10-x) outlet pipes
Part of tank filled by x inlet pipes = 1/12 [(10-x)/8]-[x/6] = 1/12
Solving, 3(10-x)-4x = 2
or, 30-7x=2
or, 7x=28
So, x=4
Hence, there are 4 inlet pipes and 6 outlet pipes.
