P,Q and R together can do a piece of work in 12 days.They started the work together but after 4 days P left.Q left 5 days before the completion of the work. If the work is completed in 19 days and the rate of working of R is twice that of Q,in how many days can P alone do the same work?

• Ans: 30 days
  
  1/P + 1/Q + 1/R = 1/12 ---(i)
  Given, work is completed in 19 days, P works for 4 days, Q for 14 days and R for 19 days.
  Then, 4/P + 14/Q + 19/R = 1 ---(ii)
  Also given, rate of working of R is twice that of Q => 1/R = 2/Q
  Now substituting 1/R = 2/Q in eqn. (i) & (ii), we get 1/P + 3/Q = 1/12 ---(iii) and
  4/P + 52/Q = 1 --- (iv)
  Solving eqn. (iii) & (iv), we get P=30, Q=60
  Therefore, P alone can do the same work in 30 days.
• 5 years agoHelpfull: Yes(0) No(1)