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
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Important Questions from Work Efficiency
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?
A and B together can do a piece of work in 4 days, B and C can do it in 6 days, A and C can do it in 8 days. Then A, B and C together can do the same work in :-
A can complete 50% of a work in 9 days and B can do 25% of the work in 9 days, if they work alone. If they work together then how much work (in percentage) can be completed in 6 days?
A is thrice as good a workman as B. C alone takes 48 days to paint a house. All three A, B and C working together take 16 days to paint the house. It will take how many days for A alone to paint the house?
