Five people A,B,C,D and E do a certain job . A, B and C together complete the job in 7.5 hrs ; A, C and E together complete it in 5 hrs; A, C and D together complete it in 6 hrs; B, D, and E together comple it in 4 hrs. If all te five people work together then how much time will be required to complete the job

• In 1 day
  
  In 1 hour,1/7.5 work is done which is equal to total work done by all in 1 hr
  => (1/A) + (1/B) + (1/C) = 1/7.5 --------------------(1)
  
  similarly,
  (1/A) + (1/C) + (1/E) = 1/5 -------------------------(2)
  (1/A) + (1/C) + (1/D) = 1/6 -------------------------(3)
  (1/B) + (1/D) + (1/E) = 1/4 -------------------------(4)
  
  (1) + (2) + (3) + 2*(4)
  => 3A + 3B + 3C + 3D + 3E = (1/7.5) + (1/5) + (1/6) + 2*(1/4)
  => A + B + C + D + E = 1 day
• 11 years agoHelpfull: Yes(1) No(0)
• In 3 hoursIn 1 hour,1/7.5 work is done which is equal to total work done by all in 1 hr=> (1/A) + (1/B) + (1/C) = 1/7.5 --------------------(1)similarly,(1/A) + (1/C) + (1/E) = 1/5 -------------------------(2)(1/A) + (1/C) + (1/D) = 1/6 -------------------------(3)(1/B) + (1/D) + (1/E) = 1/4 -------------------------(4)(1) + (2) + (3) + 2*(4) => 3/A + 3/B + 3/C + 3/D + 3/E = (1/7.5) + (1/5) + (1/6) + 2*(1/4)=> In 1 hour,1/A + 1/B 1/C + 1/D + 1/E = 1/3 work done
  
  => Total time taken = 3 hours
• 11 years agoHelpfull: Yes(0) No(0)
• 2.2 hours
  
• 11 years agoHelpfull: Yes(0) No(0)