Tushar takes 6 hours to complete a piece of work, while Amar completes...
Work done by Tushar and Amar
Let's assume that the total work to be done is represented by 1 unit.
Tushar takes 6 hours to complete the work, so his work rate is 1/6 units per hour.
Amar takes 10 hours to complete the work, so his work rate is 1/10 units per hour.
Work done when working together
When Tushar and Amar work together, their work rates add up. Therefore, the combined work rate when they work together is:
1/6 + 1/10 = (5 + 3) / 30 = 8/30 = 4/15 units per hour.
This means that when they work together, they can complete 4/15 units of work in 1 hour.
Time required to complete the work
To find the time required to complete the work, we can use the formula:
Time = Work / Rate.
In this case, the work to be done is 1 unit, and the combined work rate when Tushar and Amar work together is 4/15 units per hour.
Therefore, the time required to complete the work when they work together is:
Time = 1 / (4/15) = 15/4 = 3.75 hours.
Since 0.75 hours is equal to 45 minutes, the time required to complete the work when Tushar and Amar work together is 3 hours and 45 minutes.
Therefore, the correct answer is option D) 3 hours 45 minutes.