Chetan alone can do a work in 6 days working 5 hours a day. Rashmi alone can do the same work in 2 days working 10 hours a day. How many hours do they need to work together in a day to complete the same work in 4 days?

Chetan can complete the work in 6 days working 5 hours a day.

Rashmi can complete the same work in 2 days working 10 hours a day.

Total work = Efficiency$$\times$$ Total time

Total hours Rashmi works to complete the job: 2×10 = 20 hr 

​Total hours Chetan works to complete the job: 6×5 = 30 hr

LCM of 20 and 30 = 60 

Let total work be 60 unit

Then, efficiency of Rashmi = $$\frac{60}{20}=3 \, unit/hour$$ 

efficiency of Chetan = $$\frac{60}{30}=2 \, unit/hour$$ 

Total efficiency of Rashmi and Chetan = 3+2 = 5 unit/hour

Now, Total work in 4 days is = 4$$\times$$​ 5 = 20 unit 

So, required per day hour  =  $$\frac{60}{20}= 3 \, hour$$ 

Thus, correct option is (d).