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
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?
