If A, B and C can complete a task alone in 15 days, 20 days and 25 days. respectively, then in how many days can they complete the same task if they work together?

Correct option is A

Given:

A can complete the task in 15 days,

B can complete the task in 20 days, 

C can complete the task in 25 days, 

Formula Used:

$$\text{Total work rate} = \frac{1}{A} + \frac{1}{B} + \frac{1}{C}, \\ \ \\ \text{Time to complete the task} = \frac{1}{\text{Total work rate}}.$$​

Solution: 

 A's work rate is $$\frac {1}{15}$$​  per day

 B's work rate is $$\frac {1}{20}$$​​  per day.

 C's work rate is $$\frac {1}{25}$$​​  per day.

Total work rate( A + B + C) = $$\frac{1}{15} + \frac{1}{20} + \frac{1}{25}$$​

 LCM of 15, 20, and 25  = 300

Total work rate =$$\frac{20}{300} + \frac{15}{300} + \frac{12}{300} = \frac{47}{300}$$​

Time to complete the task = $$\frac{1}{\frac{47}{300}} = \frac{300}{47}$$ days

Alternate Method:

Total work = Efficiency $$\times$$ Time

 LCM of 15, 20, and 25  = 300 

Efficiencies of A = $$\frac{300}{15}$$​ = 20 , B = $$\frac{300}{20}$$= 15,  C = $$\frac{300}{25}$$ = 12

Time taken together by A + B + C = $$\frac{300}{20 +15+12} = \frac{300}{47} \ days$$​​