souvonik2k wrote:

X, Y and Z together can complete a job in 10 days. The rate of work of X is three times that of Y, which, in turn is twice that of Z. What is the time taken by Z alone to complete the job?

A) 30 days

B) 60 days

C) 90 days

D) 120 days

E) 180 days

Let RX = rate of X

RY = rate of Y

RZ = rate of Z

RX = 3RY & RY = 2RZ & then RX = 6RZ

Apply in formula:

Rate * Time = Work

(RX + RY + RZ) 10 = 1

From above:

6RZ + 2RZ + RZ = 1/10...........9RZ = 1/10.........RZ = 1/90

Inverse of the rate of Z will yield the time Z takes to complete the job

Time of Z = 90 days

Answer: C