P alone can complete a piece of work in 10 days while Q alone can complete the same piece of work in 15 days. To complete the work in 4 days, R is hired by P and Q. How many days does R take to complete the work alone ?
Answer & explanation
Correct answer: option 4
Efficiency ∝ $\frac{1}{time}$
P : Q
Time 10 : 15 = 2 : 3
Efficiency 3 : 2
Let the total work be 30
To complete this work in 4 days, R is hired with efficiency (say, r)
Thus, using the formula
Efficiency × Days = Total work
(3 + 2 + r) x 4 = 30
20 + 4r = 30
r = 2.5
Time taken by R alone to complete the work = $\frac{Total\;work}{efficiency}$ = $\frac{30}{2.5}$
= 12 days