Pipes A, B and C can fill a tank in 30, 60 and 120 minutes respectively. Pipes B and C are kept open for 10 minutes, and then Pipe B is shut while Pipe A is opened. Pipe C is closed 10 minutes before the tank overflows. How long does it take to fill the tank?
Choose the correct answer:
A) 40 minutes B) 28 minutes C) 30 minutes D) 36 minutes E) 34 minutes
DETAILED SOLUTION   Let us assume that the tank has a capacity of 120 litres. So, the pipes discharge the following amounts of water:   (A) 4 litres per minute   (B) 2 litres per minute   (C) 1 litre per minute.   Part 1: B and C (3 litres/min) are kept open for 10 minutes, filling 3 × 10 = 30 litres. 90 litres remain to be filled in the tank.   Part 2: Now, B is shut and A is opened. Effectively, this means that A and C are filling the tank together (5 litres / minute). We don’t yet know how long A and C are open together.   Part 3: C is closed 10 minutes before the tank overflows. This means that only A works for the last 10 minutes, filling 40 litres (working@4 litres/min)   Since 30 litres are filled in Part 1 and 40 litres in Part 3, the balance (50 litres) should have been filled in Part 2.   Working together, A and C fill 5 litres per minute in Part 2. This means that they would have taken 10 minutes to fill 50 litres.   So, the entire time it took to fill the tank is:   10 + 10 + 10= 
<gadget id="calculator">10 + 10 + 10</gadget>
<output>30</output>
30 mins.   Answer choice (c)   Alternate Solution   In one minute, A fills (1/30)th of the tank, B fills (1/60)th of the tank, and C fills (1/120)th of the tank.   (B + C) work for 10 minutes, followed by (A + C), which works for “t” minutes, followed by A, which work for 10 minutes. This ensures that the tank gets filled. This can be written in an equation form:   10 x (1/60 + 1/120) + t x (1/30 + 1/120) + 10 x (1/30)= 1   10 x (1/40) + t x (1/24) + 10 x (1/30) = 1.   Or, 1/4 + t/24 + 1/3 = 1. Or t = 10.   So, the entire tank was filled in 30 mins.   Answer choice (30 minutes).
<result>C</result>
Pipes A, B and C can fill a tank in 30, 60 and 120 minutes respectively. Pipes B and C are kept open for 10 minutes, and then Pipe B is shut while Pipe A is opened. Pipe C is closed 10 minutes before the tank overflows. How long does it take to fill the tank?