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?
- 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?
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?
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- 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.
- 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?
- 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:
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Important Questions from Work Efficiency
Sumi can complete a job working 5 hours per day in 2 days. If she doubles her working hours per day, then in how many days will she complete the work?
Five men and 2 boys can do in 30 days as much work as 7 men and 10 boys can do in 15 days. How many boys should join 40 men to do the same work in 4 days?
A man completes 7/8 of a job in 21 days. How many more days will it take him to finish the job if quantum of work further increased by 50%?
24 men and 12 women can do a piece of work in 30 days. In how many days can 12 men and 24 women do the same piece of work?
3 men working 7 hours a day can complete a piece of work in 45 days. In how many days will 9 men working 6 hours a day complete the same work?
