P alone can do a piece of work in 5 days and Q alone in 4 days. P and Q undertook to do it for ₹3000. With the help of R they completed the work in 2 days. How much is to be paid to R?

₹300

Total work = efficiency × time ⇒ Efficiency = \(\frac{Total\;work}{time}\)

Let total work = 20  (LCM of time 5, 4 & 2 days)

Efficiency of P = \(\frac{20}{5}\) = 4 w/d

Efficiency of Q = \(\frac{20}{4}\) = 5 w/d

If all of them complete the work in 2 days, then the total efficiency (P + Q + R)

worked = \(\frac{20}{2}\) = 10 w/d

Therefore,

Efficiency of R = 10 - 4 - 5 = 1 w/d

Ratio of Efficiency (P : Q : R) = 4 : 5 : 1

Note: When all the person work for the same time, then the amount should be distribute in the ratio of their efficiency.

Hence,

P : Q : R = 4 : 5 : 1 = 10 (total)

10R = Rs.3000

1 R = Rs.300

R's share = 1R = Rs.300/-