To finish a piece of work,P takes Five times as Q and six times as R. Working together, they can finish the work in 4 days. Q can do the work alone in:

• Time taken by p:q => 5q:q
  Time taken by p:r => 6r:r
  5q = 6r
  q=6r/5
  Time taken by p:q:r => 6r:6r/5:r
  p+q+r's 1 day work = 1/4
  1/6r + 5/6r + 1/r = 1/4
  (1+5+6)/6r = 1/4
  6r=48
  r = 8
  p => 6r = 6*8 = 48
  q => 6r/5 = 6*8/5 = 48/5 days
  
  Q can finish the work alone in 48/5 days => 9.6 days
  
  Ans : 9.6 days
• 10 years agoHelpfull: Yes(36) No(1)
• suppose that P takes x days to finish a work then Q=x/5 and R=x/6 days to finish that work.
  now P's 1 day work=1/x
  Q's 1 day work=5/x
  R's 1 day work=6/x
  (P+Q+R)'s 1 day work=12/x
  (P+Q+R)'s 4 day work=48/x
  but 4th days finish the work so x=48
  so P=48 Q=9.6 R=8
• 10 years agoHelpfull: Yes(8) No(3)
• as given
  P=5Q P=6R
  so,let Q takes x days for it then we can write
  1/5x+1/x+6/5x=12/5x as work done by P,Q,R in one day
  so,5x/12=4 according to ques
  x=48/5 and this is the time taken by Q
  
• 10 years agoHelpfull: Yes(6) No(1)
• as given
  
  p=5q.....(1)
  p=6r.......(2)
  
  they working together so = 1/p+1/q+1/r=1/4 ....(3)
  in above equation we get the r,q value so
  q=p/5...(4)
  r=p/6...(5)
  
  put the q,r value in equation 3
  1/p+5/p+6/p=1/4
  12/p=1/4
  p=48
  put p value in equation 4
  q=48/5
  q=9.6 ans
• 10 years agoHelpfull: Yes(3) No(0)