Working 5 hr day, A can complete a task in 8 days and working 6 hr a day, B can complete the same task in 10 days. Working 8 hr day, they can jointly complete the task in:

Correct option is C

Given

A can complete the task in 8 days, working 5 hours/day.

B can complete the task in 10 days, working 6 hours/day.

To find: the time taken by A and B together to complete the task, working 8 hours/day

Formula Used

Work = Time × Rate of work

Solution
Let the total work be W units.

A's total hours to complete the task: 8 days × 5 hours/day = 40hours.

A's work rate per hour = $$\frac{W}{40}$$​ ​units/hour.

B's total hours to complete the task =10 days × 6 hours/day = 60 hours

B's work rate per hour: B’s rate = $$\frac{W}{60}$$​ units/hour

combined work rate per hour:

Combined rate = $$\frac{W}{40} + \frac{W}{60} = \frac{3W}{120} + \frac{2W}{120} = \frac{5W}{120} = \frac{W}{24}$$​​
In 1 day, working 8 hours, their combined work done is:

​$$8 \times \frac{W}{24} = \frac{8W}{24} = \frac{W}{3}$$​​
Since, they complete $$\frac{W}{3}​$$​ of the work per day, the total time taken is:

Time = $$\frac{W}{\frac{W}{3}}$$​ = 3 days.