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Three machines A, B and C are set to work together. A working alone takes 6 hours to complete the work; B takes 8 hours while C takes 12 hours. All the three machines started working at the same time. 40 minutes later machine A broke down. B and C continued for another 1 hour before B ran out of fuel and therefore stopped working for 20 minutes while C continued. If B resumed working after 20 minutes, calculate the:

  1. Fraction of the work left after machine A broke down.
  2. Fraction of the work done by C working alone for 20 minutes 
  3. Total time taken for the work to be completed. 

1 Answer

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  1. 1/6 + 1/8 + 1/12 = 3/8
    40/60 x 3/8 = 1/4
    = 1 - 1/4 = 3/4
     
  2. 1hr    = 1/12
    20min = ?
    20/60 x 1/12 = 1/36
     
  3. B & C = 1/8 + 1/125/24
    3/4 - 5/24 = 13/2413/24 - 1/36 = 37/72
    5/24 = 1hr
    37/72 = 37/72 x 24/5 = 27/15
    time= 40minutes + 1hr 20 mins + 2hrs 28mins
    =4hrs 28min

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