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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?

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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?


1). Rs. 3000
2). Rs. 4500
3). Rs. 6000
4). Rs. 7200


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Answered by on | Votes 0 |

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

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