Pipe L can empty the tank which is 45% filled in 9

Solution

Let’s assume the total capacity of the tank is 60 units.

Pipe L can empty the tank which is 45% filled in 9 hours.

Time taken by pipe L alone to empty the tank which is completely filled = (9/45)x100

= 20 hours

Efficiency of pipe L = 60/20 = -3 units/hour (Here negative sign represents that the pipe is used to empty the tank.)

The ratio between the efficiencies of pipe J and M is 3:2 respectively.

Let’s assume the efficiencies of pipe J and M are ‘3a‘ and ‘2a‘ respectively.

The efficiency of pipe K is one third of the efficiency of pipe J.

efficiency of pipe K = ⅓ of 3a = a

The time taken by pipe K and J together to fill an empty tank completely in 7.5 hours.

7.5(a+3a) = 60

(a+3a) = 8

4a = 8

a = 2

Pipe J alone can fill an empty tank completely in (z-5) hours.

efficiency of pipe J = 3a = 3x2 = 6 units/hour

So 6x(z-5) = 60

(z-5) = 10

z = 10+5

Value of z = 15