P and Q can do a job in 90 days, Q and R can do it in 112.5 days, while P and R can do it in 150 days. X is five times as efficient as P, Y is two-thirds as efficient as Q, and Z is 2.5 times as efficient as R. Determine the number of days required to complete the same job if X, Y and Z work together.

Correct option is A

Given:
P and Q can do the job in 90 days.
Q and R can do the job in 112.5 days.
P and R can do the job in 150 days.
X is 5 times as efficient as P.
Y is $$\frac{2}{3}$$​ as efficient as Q.
Z is 2.5 times as efficient as R.
Formula Used:

Total Work = Efficiency $$\times$$ Total Time

Solution:

2(P + Q + R) = 5 + 4 + 3

P  + Q + R = $$\frac{12}{2}$$​  = 6

Efficiency of P + Q + R = 6

So, efficiency of P, Q , R:

P = 2 , Q = 3 , R = 1

Then,

Since Efficiency is double to removing the fraction, So Total work also be double:

Total Work = 450 $$\times$$ 2 = 900

Efficiency of  (X + Y + Z) = 29

The number of days required to complete the same job if X, Y and Z work together.

Required Time  =  $$\frac{900}{29}$$ days or $$31\frac{1}{29}$$ Days

Thus, the correct option is (a)