Problem Solving

There are four outlet pipes of the same capacity fixed one above the other to a water tank. The first pipe is at the bottom level and the fourth pipe is at three-fourths of the height of the tank. The third pipe is equidistant from the second pipe and the fourth pipe, the second pipe is equidistant from the first and the third. The capacity of each pipe is such that it can empty a full tank in four hours, whereas one inlet pipe can fill the empty tank in one hour. The pipe is opened to fill the empty tank and after one hour it is closed, then all the outlet pipes are opened When the tank is full, all the four pipes are opened together and shut after one hour. If the inlet pipe is opened now, the time in which the tank will be full is :

(A). 60 minutes (B). 42.5 minutes
(C). 17.5 minutes (D). 10 minutes

The four outlet pipes are at the following positions:
4th one at the bottom most
3rd one at 1/4th height from bottom
2nd one at 1/2 the height from bottom
1st one at 3/4th height from bottom

The inlet pipe fills the tank to full in an hour's time.
Each outlet pipe can empty in 4 hr => all four at a time can empty in 1 hr
If 3 pipes are working at a time, the can empty in 4/3 hr
If 2 pipes are working at a time, the can empty in 4/2 hr
After vacating the top 1/4th portion, the effect of top most pipe is not considered as the water level reaches it's height.Similarly, after vacating 1/2 of the portion, the effect of top-second pipe is also not considered as such the effect of top-thrid pipe after vacating 3/4th portion.
The top-most pipe is at a distance of 1/4th height from top => first 1/4th portion is emptied by all the four pipes in 1/4 * 1 = 1/4 hr
The top-second pipe is at a distance of 1/4th height from the top-first pipe => second 1/4th portion is emptied by the remaining three pipes in 1/4 * 4/3 = 1/3 hr
The top-3rd pipe is at a distance of 1/4th height from the top-2nd pipe => third 1/4th portion can be emptied by the remaining two pipes in 1/4 * 4/2 = 1/2 hr. But After emptying the first two fourths, the time left out
= 1-(1/4 + 1/3) = 5/12 hr , which is less than 1/2 hr.
The remaining two pipes can empty (5/12)/(4/2) = 5/24th portion.
Conclusion:
After 1hr time, the portion of tank with water = 1-(1/4 + 1/4 + 5/24) = 7/24th
=> The portion to be filled by the inlet pipe = 1 - 7/24 = 17/24
The inlet pipe can fill the tank to full in 1 hr => it can fill 17/24th of tank in 17/24 hr
= 17/24 * 60 min = 42.5 min
Answer "B"