Work Rate Calculation: Vinod's Solo Completion
This problem requires calculating individual work duration based on relative efficiencies and combined work time.
Understanding Work Rates
- Let the rate at which Vinod works be '$V$' units per day.
- Raju is thrice as good as Vinod, meaning Raju's work rate '$R$' is $3V$ units per day.
Combined Work Efficiency
- When working together, their combined rate is the sum of their individual rates: $R + V$.
- Substituting Raju's rate: $3V + V = 4V$ units per day.
Determining Total Work
- Raju and Vinod can finish the task together in 21 days.
- The formula for total work is: Total Work = Combined Rate $\times$ Time.
- Total Work = $(4V \text{ units/day}) \times (21 \text{ days})$
- Total Work = $84V$ units.
Vinod's Solo Completion Time
- To find the number of days Vinod takes to complete the work alone ($D_V$), we use: Total Work = Vinod's Rate $\times$ $D_V$.
- $84V \text{ units} = V \text{ units/day} \times D_V \text{ days}$
- Solving for $D_V$: $D_V = \frac{84V}{V}$
- $D_V = 84$ days.
Therefore, Vinod can complete the work alone in 84 days.
Similar Questions
- 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?
- Kamal can complete a work in 14 days. Vimal is 40% more efficient than Kamal. The number of days Vimal will take to complete the same piece of work is:
- 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?
