P, Q and R together can complete a work in 40 days. P and Q together can complete the same work in 90 days. Then R alone can complete the same work in how many days ?

(P + Q + R)’s 1 day’s work $=\frac{1}{40}$ $(\mathrm{P}+\mathrm{Q})$ ’s 1 day’s work $=\frac{1}{90}$ $\therefore$ R’s 1 day’s work $=\frac{1}{40}-\frac{1}{90}$ $=\frac{9-4}{360}=\frac{5}{360}=\frac{1}{72}$ $\therefore$ Required time $=72$ days Alternative:

P + Q = 4

P + Q + R = 9

∴ R = 5

Time taken by R alone to complete the work

$=\frac{\text { Total work }}{\text { Efficiency of } \mathrm{R}}=\frac{360}{5}=72$ days