Tap A alone takes 30 minutes to fill up a tank, while tap B alone takes 45 minutes to fill up the same tank. Tap C which is at the bottom of the tank can alone empty it in 36 minutes. Another tap D is fixed at 1/2 level of the tank. What will be the possible time t taken by tap D to empty the tank alone, if the tank is half full and it remains half full always when all four taps are open?Indicate all such values
A. T = 37 minutes B. T = 18 minutes C. T = 45 minutes D. T = 26 minutes E. T = 30 minutes
T = 18 minutes-2. t = 26 minutes-3. t = 30 minutes-ans: b, d and e (both a & b together can fill up the tank in 18 minutes (1/30 + 1/45 = 1/18)
now tap c & d should also be able to empty the tank in not more than 18 minutes for tank to remain at half level. so maximum time taken by d will be 36 minutes. (1/36 + 1/36 = 1/18)
now if c & d take less time to empty, then when all tapes are open then the level will go down from 1/2. but tap d is at 1/2 level, so it will stop working and only c will empty in 36 minutes while a & b will fill up in 18 minutes. so water level will go up & when the level is more than 1/2, then d will start working & level will start reducing. ultimately it will settle at 1/2 level only when all tapes are on. this will happen for any value of t < 36 minutes. hence 0 < t < 36 minutes.
so t will take any value less than 36 minutes.)