20. Each of A,B and C need a certain unique time to do certain work. C needs 1 hour less than A to complete the work. Working together they require 30 minutes to complete 50% of the work. The work also gets completed if A and B start working together and A leaves after 1 hour and B works further 3 hours. How much work does C do per hour?

a. 16.66%
b. 66.66%
c. 50%
d. 33.33%

• A will take 3 hrs to complete job.B .. 6 hrs
  C-- 2 hrs
  
  If A takes x hrs, B take y7 hrs and C takes x-1 hrs to complete job independently, then
  1/x +1/(x-1) +1/y =1 because they together complete 100% job in 1 hour.
  1/x +1/y + 3/y = 1
  
  solving these 2 eqns, we get
  x=3 and y=6
  
  So C complete total work in 2 hrs
  
  C will complete 50% work in 1 hr.
• 12 years agoHelpfull: Yes(28) No(4)
• answer is D.:66.66%
• 12 years agoHelpfull: Yes(4) No(9)
• can u xpln
• 12 years agoHelpfull: Yes(3) No(7)
• Let A take 'a' hours to complete the work alone.
  Then C takes (a-1) hours to complete the work alone.
  In 1 hour 'A' completes 1/a of the work.
  In 1 hour 'C' completes 1/(a-1) of the work.
  Both together complete 1/a + 1/(a-1) = (2a-1)/a(a-1) of the work in 1 hour.
  A & C together need a(a-1)/(2a-1) hours to complete the work.
  Now A & C together complete 50% of work in 30 minutes
  So A & C together complete 100% work in 1 hour.
  Therefore a(a-1)/(2a-1) = 1
  solving, a= {3(+/-)√(5)}/2
  C takes one hour less than A to complete the work, which can not be -ve. So we can discard a=(3 - √5)/2 .
  Hence a=(3 + √5)/2 .
  So 'C' takes (a-1) = (1+√5 )/2 hours to complete the work.
  In one hour 'C' will complete 2/(1+√5 ) = 2/3.24 = 0.66 of work
  = 66%
• 12 years agoHelpfull: Yes(3) No(4)