P, Q, R can do a piece of work in 40 days, 90 days and 36 days, respectively. P started the work. Q joined him after 7 days. If R joined them after 8 days from the beginning, then for how many days did R work?

Correct option is B

Given:

P, Q, R can do a piece of work in 40 days, 90 days and 36 days, respectively.
P started the work. Q joined him after 7 days. If R joined them after 8 days from the beginning
Formula Used:
Total work = Efficiency × Total time taken
Solution:
LCM (40, 90, 36) = 360
Let the total work be the LCM of the time taken individually by the workers.
Efficiencies,
P does each day = 360 ÷ 40 = 9 units
Q does each day = 360 ÷ 90 = 4 units
R does each day = 360 ÷ 36 = 10 units
Let the total work will be completed in K days.
According to the question,
9 × K + 4 × (K - 7) + 10 × (K - 8) = 360
=> 23K = 468
=> K = 468/23
=> (K - 8) = 284/23 = $$12 \frac {8}{23}$$ days​
R worked for 12$$\frac{8}{23}$$ days​