Three workers, X, Y and Z, can finish a job in 6 days, 9 days and 18 days, respectively. How long will it take them to finish the job if they all work together?

Correct option is A

Given:

Worker X can finish the job in 6 days

Worker Y can finish the job in 9 days

Worker Z can finish the job in 18 days

Formula Used:

Work done by a worker in 1 day =$$\frac{1}{\text{time taken to finish the job}}$$​​

Solution:
The rate of work of each worker is:

X's work rate $$= \frac{1}{6}$$​ of the job per day

Y's work rate $$= \frac{1}{9}$$​ of the job per day

Z's work rate =$$\frac{1}{18}$$​ of the job per day

Total work rate when they work together:

Total work rate $$= \frac{1}{6} + \frac{1}{9} + \frac{1}{18}$$​

​$$\text{Total work rate} = \frac{3}{18} + \frac{2}{18} + \frac{1}{18} = \frac{6}{18} = \frac{1}{3}$$​

Thus, they will finish the job in 3 days when they work together.

Alternate Method:

Total Work = 18 (lcm of 6, 9 and 18)

Efficiency of worker X = 3

Efficiency of worker Y = 2

Efficiency of worker Z = 1

Time taken if they work together = $$\frac{18}{3+2+1}=\frac{18}{6}=3$$ days​