Anil alone takes 2 hrs 40 min to complete a work and sumit alone can complete the same work in half time of Anil How much time will be taken by sumit to complete the work?
80 mins
Calculating Work Time for Anil and Sumit
This problem involves calculating the time taken by two individuals, Anil and Sumit, to complete a specific work. We are given the time Anil takes and the relationship between Anil's time and Sumit's time.
Understanding the Given Information
- Anil alone takes 2 hours and 40 minutes to complete the work.
- Sumit alone can complete the same work in half the time taken by Anil.
We need to find the time Sumit takes to complete the work in minutes.
Convert Anil's Work Time to Minutes
First, let's convert Anil's total work time from hours and minutes into minutes.
We know that 1 hour = 60 minutes.
Anil's time = 2 hours + 40 minutes
Anil's time in minutes = $(2 \times 60)$ minutes + 40 minutes
Anil's time in minutes = $120$ minutes + 40 minutes
Anil's time in minutes = $160$ minutes
Determine Sumit's Work Time
The problem states that Sumit takes half the time Anil takes to complete the work.
Sumit's time = $\frac{1}{2} \times$ Anil's time
Sumit's time = $\frac{1}{2} \times 160$ minutes
Sumit's time = $\frac{160}{2}$ minutes
Sumit's time = $80$ minutes
Therefore, Sumit will take 80 minutes to complete the work alone.
Revision Table: Work and Time Concepts
| Concept | Description | Relationship |
|---|---|---|
| Work | The total task to be completed. Often considered as 1 unit of work. | Work = Rate $\times$ Time |
| Time | The duration taken to complete the work. | Time = $\frac{\text{Work}}{\text{Rate}}$ |
| Rate (Efficiency) | The amount of work done per unit of time. | Rate = $\frac{\text{Work}}{\text{Time}}$ |
Additional Information: Understanding Work Rate
In work and time problems, the concept of work rate is very useful. The rate of work is inversely proportional to the time taken to complete the work. This means if someone takes less time, they have a higher work rate (are more efficient), and if they take more time, they have a lower work rate.
Let's consider the work rate for Anil and Sumit:
Assume the total work is 1 unit.
- Anil's time = 160 minutes.
- Anil's work rate = $\frac{\text{Work}}{\text{Time}} = \frac{1}{160}$ work per minute.
- Sumit's time = 80 minutes.
- Sumit's work rate = $\frac{\text{Work}}{\text{Time}} = \frac{1}{80}$ work per minute.
Notice that Sumit's rate ($\frac{1}{80}$) is double Anil's rate ($\frac{1}{160}$), which makes sense because Sumit takes half the time to complete the same work.
Important Questions from Time and Work
Surbhi can do a piece of work in 24 days. She completed 3/8 of the work and then left it. Amit can complete the remaining work in 10 days. Working together, they will complete 125% of the same work in:
Rama and Hari can together finish a piece of work in 15 day. Rama works twice as fast as Hari, then Hari alone can finish work in :
Anil, Deepak and Dinesh together can complete a work in 35 days. Anil and Dinesh together can complete the same work in 60 days. In how many days Deepak alone can complete the same work?
Anu is four times as good as Binni in completing a task. Together they finish the same task in 7 hours. In how many hours will Anu alone complete the task?
P, Q and R can complete a work in 10 days, 20 days and 30 days, respectively, working alone. How soon can the work be completed if P is assisted by Q and R on alternate days?
