Question 8

# Pipe A can empty filled tank in 28 hours while Pipe B can fill the same tank, whenempty, in 35 hours. If alternately Pipes A and B are turned on for an hour each time, starting when the tank is full, how long will it take to empty the tank?

Solution

LCM(28, 35) = 140 litres is the total capacity of tank.

A pipe empties 5 liters in 1hour and Pipe B fills 4 liters in 1hour.

In 2 hours A and B pipes empties 1 liter.

[ It can understand by,

A’s 1 hour work and B's next hour( 2nd hour) work,

i.e, ($$\frac{-1}{28}$$)+($$\frac{1}{35}$$)

=$$\frac{-1}{140}$$

From this we can easily conclude that,

Every 2 hours empties both pipes together 1 liter.

For emptying full tank of 140litre takes,

If pipe A was started emptying the tank first

For emptying of 135 liters takes time 2x135 = 270 hours and remaining 5liters emptied in 1hour by pipe A