Anna, Benne and Cenna are have friends. Anna and Benne are twins. Benne takes 2 days more than Cenne to complete the work. If Anne started a work and 3 days later Benne joins him then the work gets complete in 3 more days. Working together . Anne, Benne and Cenne can complete thrice the original work in 6 days. In how many days Benne can complete twice the original work with double the efficiency working alone?

• Ans: 6 days
  
  Working alone, let Anna, Benne and Cenna can complete the work in A, B & C days respectively, then
  
  Statement I) : Benne takes 2 days more than Cenne => B=C+2 ---(i)
  
  Statement II) : Anne started a work and 3 days later Benne joins him then the work gets complete in 3 more days => When Anne worked for 6 days & Benne for 3 days, work gets completed.
  => 6/A + 3/B = 1 ---(ii)
  
  Statement III) : Anne, Benne and Cenne can complete thrice the original work in 6 days.
  => Together they can complete the original work in 2 days.
  => 1/A + 1/B + 1/C = 1/2 ---(iii)
  
  Now solving (ii) & (iii), we get 3/B + 6/C = 2 ---(iv)
  Substituting C=B-2 from (i) in eqn (iv), 3/B + 6/(B-2) = 2
  3B - 6 + 6B = 2(B² - 2B)
  2B² - 13B + 6 = 0
  (2B-1) (B-6) = 0
  B=1/2, 6. Considering whole number of days, B=6
  
  Now B's 1 day work=1/6. With twice efficiency 1 day's work = 2/6 = 1/3
  Therefore, days required for twice the original work = 2/(1/3) = 6
• 5 years agoHelpfull: Yes(2) No(1)