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28 Oct 2022 : Pipes & Cisterns

Pipes A and B are fitted to a tank. A can fill the tank in 1½ hours and capacity of B which is emptying pipe is half that of A. If B is fitted at one-third of the height of the tank from the base and both the pipes are opened simultaneously, then time taken to fill the empty tank is:

OPtion

1) 2 hours
2) 3 hours
3) 1 hour 50 minutes
4) 2 hours 15 minutes
5) 1 hour 45 minutes
6) 2 hours 24 minutes
7) 1 hour 56 minutes
8) 2 hours 30 minutes
9) 2 hours 45 minutes
10) None of these

Solution

Filling capacity of A per hour = 2/3, .'. Emptying capacity of B per hour = (1/2)*(2/3) = 1/3
As B, the emptying pipe is fitted at 1/3 of the height of the tank from base, so the draining will start only after tank is 1/3 full.
Now time taken to fill 1/3 tank by A = (1/3)/(2/3) = 1/2 hrs.
Effective filling per hour after 1/3 tank is full = 2/3 - 1/3 = 1/3
.'. Time required to fill remaining 2/3 tank = (2/3) / (1/3) = 2 hrs
Total time = (1/2 + 2) Hrs = 2 hours 30 minutes
Correct Option 8)

Correct Option: 8 Best Solution (1)

Best user's solution

G.S.Kantharao

A can fill =1&1/2hr
1/3 rd can be filled in 1/2
B can empty in 3/4 hr
Remaining 2/3 can empty by
=(3/4)*(2/3)=1/2
Remaining 2/3 can fill by A=1hr
So in 1hr it can be filled =1-1/2=1/2
So the whole tank can be filled at 2hrs+1/2hr=2hrs.30m
My option is 8👈

Is this solution helpfull? Yes (10) | No (1)