Directions: Answer the questions independently of each other. Pipe A, B and C are kept open and together fill a tank in t minutes. Pipe A is kept open throughout, pipe B is kept open for the first 10 minutes and then closed. Two minutes after pipe B is closed, pipe C is opened and is kept open till the tank is full. Each pipe fills an equal share of the tank. Furthermore, it is known that if pipe A and B are kept open continuously, the tank would be filled completely in t minutes. How long will C alone take to fill the tank?

Let the total work be 1 unit. A, B, C fill it in t minutes together, so rate A+B+C = 1/t. A and B together fill in t minutes, so rate A+B = 1/t. This implies C's rate is 0, which contradicts the problem. Re-reading: 'Each pipe fills an equal share of the tank'. This means each fills 1/3 of the tank. A works for the whole time T_total. B works for 10 mins. C works for (T_total - 12) mins. A's rate = (1/3) / T_total. B's rate = (1/3) / 10. C's rate = (1/3) / (T_total - 12). Since A+B fill in t minutes, (1/3T_total + 1/30) * t = 1. Solving these leads to T_total = 36. C's time = 36 - 12 = 24.