Dhiraj's Work Days Calculation
This section details how to calculate the number of days Dhiraj can complete a piece of work individually, given combined work information and Dhaval's solo work time.
Work Rates: Dhaval and Dhiraj
We assume the total work required is 1 unit. The rate of work represents the fraction of this unit completed per day.
- Combined rate of Dhaval and Dhiraj: Since they finish the work together in 12 days, their combined rate is $ \frac{1}{12} $ units per day.
- Dhaval's individual rate: Dhaval completes the work alone in 20 days, so his rate is $ \frac{1}{20} $ units per day.
Dhiraj's Rate Calculation
To find Dhiraj's individual rate, we subtract Dhaval's rate from their combined rate.
$ \text{Dhiraj's Rate} = \text{Combined Rate} - \text{Dhaval's Rate} $
$ \text{Dhiraj's Rate} = \frac{1}{12} - \frac{1}{20} $
Finding a common denominator (60) allows for subtraction:
$ \text{Dhiraj's Rate} = \frac{5}{60} - \frac{3}{60} = \frac{2}{60} = \frac{1}{30} $ units per day.
Dhiraj's Time Calculation
The time Dhiraj needs to complete the work alone is the reciprocal of his daily rate.
Time for Dhiraj = $ \frac{1}{\text{Dhiraj's Rate}} = \frac{1}{\frac{1}{30}} $ days.
Time for Dhiraj = 30 days.
Similar Questions
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Important Questions from Time and Work
A and B can do a piece of work in 18 days. B and C together can do it in 30 days. If A is twice as good a workman as C, find in how many days B alone can do the work?
Two men and 7 women can complete a work in 28 days, whereas 6 men and 16 women can do the same work in 11 days. In how many days will 5 men and 4 women, working together, complete the same work?
A man and a woman, working together can do a work in 66 days. The ratio of their working efficiencies is 3 ∶ 2. In how many days 6 men and 2 women together can do the same work?
Each one of five men independently can complete a work in 20 days. The work is started by one person. Next day one more person joins and every next day one more person joins. From the fifth day, five persons continued working as a team. In how many days, will the work be completed?
Numan does half the work as Gagan in 4/5 of the time. If together they take 16 days to complete a piece of work, then how long will it take Gagan to complete the work?
