Work Efficiency Solution Analysis
The question asks for the number of days Vimal will take to complete a work, given that Kamal completes it in 14 days and Vimal is 40% more efficient than Kamal.
Efficiency and Time Relationship
Efficiency and the time taken to complete a fixed amount of work are inversely proportional. This means if someone is more efficient, they take less time.
Mathematically, Work = Efficiency × Time. For the same amount of work:
$ \frac{\text{Time}_1}{\text{Time}_2} = \frac{\text{Efficiency}_2}{\text{Efficiency}_1} $
Calculating Vimal's Time
Let $E_K$ be Kamal's efficiency and $E_V$ be Vimal's efficiency.
Vimal is 40% more efficient than Kamal:
$ E_V = E_K + 0.40 \times E_K = 1.40 \times E_K $
Let $T_K$ be the time taken by Kamal (14 days) and $T_V$ be the time taken by Vimal.
Using the inverse relationship:
$ \frac{T_K}{T_V} = \frac{E_V}{E_K} $
Substitute the known values:
$ \frac{14 \text{ days}}{T_V} = \frac{1.40 \times E_K}{E_K} $
$ \frac{14}{T_V} = 1.40 $
$ \frac{14}{T_V} = \frac{140}{100} = \frac{14}{10} $
Solving for $T_V$:
$ T_V = 14 \times \frac{10}{14} $
$ T_V = 10 \text{ days} $
Therefore, Vimal will take 10 days to complete the same piece of work.
Similar Questions
- Raju is thrice as good as a workman as Vinod and together they can finish a task in 21 days. In how many days can Vinod alone complete the work?
- A can do $\frac{1}{5}^{\text{th}}$ of some work in 12 days, B can do $20\%$ of the same work in 10 days, C can do $\frac{1}{6}^{\text{th}}$ of the work in 8 days and D can do $\frac{1}{5}^{\text{th}}$ of the work in 12 days. Who will complete the work first if all four started to work at the same time?
- If Raju is thrice as good workman as Ravi and takes 20 days less than him to complete a piece of work, then find the time taken by Ravi to complete the work.
- Raj is 60% more efficient than Sundar and Sundar can finish a certain task in 16 days. How many days will Raj alone take to complete the same task?
- John is only 40% as efficient as Jesse. If John alone can do a piece of work in 35 days, how many days will it take the duo to complete the work, if they work together?
- A can do a certain work in 45 days. B is 50% more efficient than A, and C is 3 times as fast as A. They started the work together but C left 7 days before completion of the work. In how many days was the entire work completed?
- 21 women can complete a task in 40 days. 30 men can complete the task in 21 days. What is the ratio of the number of days a man will take to complete the task alone to the number of days a woman will need to do that task?
Manoj is twice as efficient a fisherman as Anuraj, and together they complete a piece of work in 22 days. In how many days can Anuraj alone complete the same work?
- Five women can do a work in thirty six days. If the ratio between the capacity of a man and a woman is 3:1, then find how many days it will take 5 men to complete the same work?
- If 15 persons can do a job in 30 days, then 30 persons with twice the efficiency can do the same job in how many days?
Important Questions from Work Efficiency
A and B together can complete a certain work in 20 days whereas B and C together can complete it in 24 days. If A is twice as good a workman as C, then in what time will B alone do 40% of the same work?
14 men can complete a work in 15 days. If 21 men are employed, then in how many days will they complete the same work?
A can do a certain work in 15 days, while B can do the same work in 21 days. If they work together, then in how many days will the same work be completed?
To do a certain work, A and B work on alternate days with B beginning the work on the first day. A alone can complete the same work in 24 days. If the work gets completed in \(11 \frac{1}{3}\) days, then B alone can complete \(\rm \frac{7}{9}^{th}\) part of the original work in:
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 can 7 men complete the same work?
