1. A tap can fill a tank in 4 hours. After half the tank is filled, 6 more similar taps are opened. What’s the total time taken to fill the tank?
Solution:
The time taken for 1 tap to fill the tank = 2 hours.
The part filled by all the 6 taps in 1 hour = 6(1/4) = 3/2.
Remaining part to be filled = 1-1/2 = 1/2.
3/2: 1/2 :: 1: x
Where 3/2 and 1 is the part filled by 6 taps and the time taken by them respectively.
1/2 and x is the remaining part and the time taken to fill them respectively.
From the above ratio, we get x = 1/2*1 *2/3 = 1/3.
In minutes, 1(60)/3 = 20 minutes.
Total time taken by them = 2+20 = 2 hours 20 minutes.
2. 3 pipes A, B and C can fill a tank in 8 hours. After working it for 2 hours, C is closed and A and B can fill the remaining part in 9 hours. The number of hours taken by C alone to fill the tank is:
Solution:
In 2 hours, the part fill is = 2(1/8) = 1/4.
Remaining part to be filled = 1- 1/4 = 3/4.
Part filled by A and B in 9 hours = 3/4.
Part filled by A and B in 1 hour = 3/4(1/9) = 1/12.
Part filled by C = 1/8 – 1/12 = 1/24.
Time taken by C = 24 hours.
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