Sangeetha Bijlani can complete a work in 16 days working 10 hours per day. Sahithya can complete the same work in 18 days working 8 hours per day. If both of them work together working 9 hours per day, in how many days can they complete the work?

Sure, let's solve this step by step.

Step 1: Calculate the total work done by each person.

Sangeetha Bijlani's total work = 16 days * 10 hours/day = 160 hours Sahithya's total work = 18 days * 8 hours/day = 144 hours

Since they are doing the same work, we can equate these two amounts of work. So, we can say that 160 hours of Sangeetha's work is equal to 144 hours of Sahithya's work.

Step 2: Calculate the rate at which each person works.

Sangeetha's work rate = 1 work / 160 hours = 0.00625 work/hour Sahithya's work rate = 1 work / 144 hours = 0.00694 work/hour

Step 3: Calculate the combined work rate when both work together.

Combined work rate = Sangeetha's work rate + Sahithya's work rate = 0.00625 work/hour + 0.00694 work/hour = 0.01319 work/hour

Step 4: Calculate the time it takes for them to complete the work together.

Time = Total work / Combined work rate = 1 work / 0.01319 work/hour = 75.78 hours

Since they are working 9 hours per day, the number of days they can complete the work is 75.78 hours / 9 hours/day = 8.42 days.

So, Sangeetha Bijlani and Sahithya can complete the work together in approximately 8.42 days when working 9 hours per day.