CBSE Class 11-science Answered

There are 4 outlet of pipes of same capacity fixed one above the other to a water tank. The 1st pipe is at the bottom level & the 4th pipe is at three-fourth of the height of the tank .The 3rd pipe is equidistant from the 2nd pipe and the 4th pipe. The 2nd pipe is equidistant from the 1st and the 3rd. The capacity of each pipe is such that it can empty a full tank in 4hr. whereas one inlet pipe can fill the empty tank in 1hr. The pipe is opened to fill the empty tank & after 1hr it is closed. Then all the outlet pipes are opened. When the tank is full all the 4 pipes are opened together and shut after 1hr. If the inlet pipe is opened now then the time in which the tank will be full is ………….min?

Asked by sunakshi | 28 Mar, 2014, 07:52: AM

Expert Answer

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

Answered by | 01 Apr, 2014, 01:01: PM