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 and 2 only
1 and 3 only
2 and 4 only
2 and 3 only

Answer 1

possible value of n is 2 and 3 only

Answer 2

The value of n is 2 or 3

Step-by-step explanation:

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

$=\frac{x}{20}-\frac{y}{30}$

$=\frac{3x-2y}{60}$

In 5 hours the tank is filled

Thus, in 5 hours, the portion filled = 1

$5(\frac{3x-2y}{60})=1$

$\implies 3x-2y=12$

$\implies x=\frac{12+2y}{3}$

$\implies x=4+2\frac{y}{3}$

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

Hope this answer is helpful.

Know More:

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