Two taps A and B can fill a water tank in 5 and 4 hours respectively. If they are turned up alternatively for one hour each (starting with tap A), find the time taken to fill the tank.


Answer:

4.5 hours

Step by Step Explanation:
  1. Tap A takes 5 hours to fill the water tank. So in 1 hour it will fill  
    1
    5
      of the tank.
  2. Tap B takes 4 hours to fill the water tank. So in 1 hour it will fill  
    1
    4
      of the tank.
  3. The tank is filled by each tap in alternate hours, starting with the tap A. So in the first hour,  
    1
    5
      of the tank will be filled, and in the second hour an additional  
    1
    4
      of the tank will be filled.
  4. We have to find out the number of hours required to fill the whole tank.
  5. So  
    1
    5
      +  
    1
    4
      +  
    1
    5
      +  
    1
    4
      + ..... = 1
    When this value equals to one, we get the number of hours the tank was filled in.
  6. Let m be the group of days (each group having 2 hours - 1 for tap A and 1 for tap B) which are needed to fill the tank).
    From above, we can write m(  
    1
    5
      +  
    1
    4
     ) = 1
    => m =  
    5 x 4
    5 + 4
      = 2.25
  7. Since m is group of 2 hours, it will 2 x m hours to fill the tank. The tank will be filled in 4.5 hours.

You can reuse this answer
Creative Commons License