Question
A fill pipe can fill a tank in 20 hours, a drain pipe can drain a tank in 30 hours. If a system of n pipes (fill pipes and drain pipes put together) can fill the tank in exactly 5 hours, which of the following are possible values of n (More than one option could be correct)?
1. 32
2. 54
3. 29
4. 40
CAT 2021
Solution
Correct option is
(D)
Explanatory Answer :
Pipe can fill a tank in 20 hours
Therefore, in one hour, the the part of the tank will be filled = 1/20
Similarly, in one hour the part of tank that can be emptied = 1/30
If there are x fill pipes and y drain pipes then
n = x+y
In one hour the portion filled
x/20 - y/ 30
= 3x-2y / 60
In 5 hours the tank is filled
Thus, in 5 hours, the portion filled = 1
5(3x-2y/60) =1
= 3x-2y=12
= x= 4+2y/3
x and y are both natural numbers here, for this y must be multiple of 3
If y = 3, x = 6
Thus, n = 9
If y = 6, x = 8
Thus, n = 14
If y = 9, x = 10
Thus, n = 19
If y = 12, x = 12
Thus, n = 24
If, y = 15, x = 14
Thus, n = 29
If y = 18, x = 16
Thus, n = 34
As per options, the value of n would be 2 or 3
