P, Q and R did a work for which they received a total of Rs. 30000. P works twice as fast as Q. Q and R together can finish a work together in one third of the time in which Q finishes the work alone. What will be the share that Q receives?
Let the efficiency Q be T.
P works twice as fast as Q.
⇒ Efficiency of P = 2T
Also, Q and R together can finish a work together in one third of the time in which Q finishes the work alone.
⇒ Efficiency of Q + Efficiency of R = 3 × Efficiency of Q
⇒ Efficiency of R = 2 × Efficiency of Q = 2T
We know, share of a person is proportional to his efficiency.
⇒ Share of Q = (Efficiency of Q/Sum of efficiencies of P, Q and R) × Rs. 30000
⇒ Share of Q = T/(2T + T + 2T) × Rs. 30000 = Rs. 6000