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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
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