The time taken by pipe B3 alone to fill an empty tank completely is half of the time taken by pipe B1 alone to fill the same tank completely. Pipe B2 alone can empty the completely filled tank in 75 hours. Pipe B2 and B3 together can fill an empty tank completely in 37.5 hours. If the efficiency of pipe B1 is 70% less than the efficiency of pipe B4, then the time taken by pipe B4 alone to fill an empty tank completely.

Solution

Let’s assume the total capacity of the tank is 150 units.

Pipe B2 alone can empty the completely filled tank in 75 hours.

Efficiency of pipe B2 = 150/75 = -2 [Here negative sign represents that the pipe is used to empty the tank.]

Pipe B2 and B3 together can fill an empty tank completely in 37.5 hours.

Efficiency of Pipe B2 and B3 together = 150/37.5 = 4 units/hour

Efficiency of Pipe B2 + Efficiency of Pipe B3 = 4

-2 + Efficiency of Pipe B3 = 4

Efficiency of Pipe B3 = 4+2 = 6

The time taken by pipe B3 alone to fill an empty tank completely is half of the time taken by pipe B1 alone to fill the same tank completely.

As we know that time is inversely proportional to efficiency. So the efficiency of pipe B3 is double the efficiency of pipe B1.

efficiency of pipe B3 = 2x efficiency of pipe B1

6 = 2x efficiency of pipe B1

efficiency of pipe B1 = 3 units/hour

If the efficiency of pipe B1 is 70% less than the efficiency of pipe B4.

3 = efficiency of pipe B4 of (100-70)%

3 = efficiency of pipe B4 of 30%

efficiency of pipe B4 = 10 units/hour

Time taken by pipe B4 alone to fill an empty tank completely = 150/10

= 15 hours