2. 100 minutes.
Problems on Pipes and cisterns:
1. Three pipes A,B and C can fill a tank from empty to full in 30, 20 and 60 minutes respectively. When the tank is empty, all the 3 pipes are opened. They discharge some solutions P, Q and R respectively. What’s the proportion of solution R in the liquid in the tank after 5 minutes?
Solution:
The part filled by them in 5 minutes = 5(1/30 +1/20 +1/60) = 1/2.
Part filled by C is 5/60 = 1/12.
The ratio will be (1/12)/ (1/2) = 6/1.
2. A large tanker can be filled by 2 pipes A and B in 10 and 40 minutes respectively. How many minutes will it take to fill the tanker from the empty state if B is used for half the time and A and B fill it together for the other half?
Solution:
Let x be the time taken to fill the tank.
Part filled by (A+B) in 1 hour = 1/10 + 1/40 = 1/8.
So, x/2 (1/8 + 1/40) = 1
x = 13(2/6) = 13(1/3) = 13 minutes 20 seconds.
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