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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

A
B
C
D
##### 2 and 3 only
Solution

Correct option is

(D)

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