Pipe L can empty the tank which is 45% filled in 9 hours. The time taken by pipe K and J together to fill an empty tank completely in 7.5 hours. Pipe J alone can fill an empty tank completely in (z-5) hours. The ratio between the efficiencies of pipe J and M is 3:2 respectively. The efficiency of pipe K is one third of the efficiency of pipe J. Find out the value of ‘z’. It is assumed that except pipe L, none of the pipe is used to empty the tank.

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