If A can complete a job in 15 days and B can complete the same job in 20 days, thenhow many days (rounded up to the nearest two decimal places) will it take for both Aand B to complete the job together?

Correct option is C

​Given:

A can complete the job in 15 days.

B can complete the job in 20 days.

We need to find the number of days it will take for both A and B to complete the job together.

Solution:

Work rate of A = $$\frac{1}{15}$$​​

Work rate of B = $$\frac{1}{20}$$​​

The total work rate of A and B working together is:

Total work rate = $$\frac{1}{15} + \frac{1}{20}$$​​

$$= \frac{4}{60} + \frac{3}{60} = \frac{7}{60}$$​

Total time taken together:

​$$= \frac{1}{\frac{7}{60}}$$​​

​$$= \frac{60}{7} \approx 8.5714 \, \text{days}$$

Alternate Solution: ​

Total Work = LCM of 15, 20 = 60

Efficiency of A = $$\frac{60}{15}$$​ = 4 units 

Efficiency of B =$$\frac{60}{20}$$​ = 3 units 

Time taken together = $$\frac{60}{7} \approx 8.57 \, \text{days}$$​​