Solving the Work and Time Problem
This problem involves calculating the time taken by individuals to complete work, both individually and together. We need to find out how long Deven would take to finish the work alone.
Calculating Individual Work Rates
First, determine the rate at which Lalit and Laxman complete the work individually.
- Lalit's time to finish work = $15\text{ days}$.
- Lalit's work rate = $ \frac{1}{15} $ of the work per day.
- Laxman's time to finish work = $25\text{ days}$.
- Laxman's work rate = $ \frac{1}{25} $ of the work per day.
Work Done Together
Next, calculate the combined work rate when Lalit and Laxman work together and the amount of work they complete in $5$ days.
- Combined work rate of Lalit and Laxman = $ \frac{1}{15} + \frac{1}{25} $.
- To add these fractions, find a common denominator, which is $75$.
- Combined rate = $ \frac{5}{75} + \frac{3}{75} = \frac{8}{75} $ of the work per day.
- Work done by Lalit and Laxman in $5$ days = $ \text{Rate} \times \text{Time} = \frac{8}{75} \times 5 $.
- Work done = $ \frac{40}{75} = \frac{8}{15} $ of the total work.
Calculating Remaining Work
Determine the amount of work left after Lalit and Laxman have worked for $5$ days.
- Total work = $1$ (representing the whole job).
- Remaining work = $ 1 - \frac{8}{15} $.
- Remaining work = $ \frac{15}{15} - \frac{8}{15} = \frac{7}{15} $ of the total work.
Finding Deven's Time
The remaining work ($ \frac{7}{15} $) is completed by Lalit and Deven in $4$ days. We need to find Deven's individual time.
- Let Deven's time to finish the work alone be $D$ days.
- Deven's work rate = $ \frac{1}{D} $ of the work per day.
- Lalit's work rate is $ \frac{1}{15} $.
- Combined work rate of Lalit and Deven = $ \frac{1}{15} + \frac{1}{D} $.
- Work done by Lalit and Deven in $4$ days = $ \left(\frac{1}{15} + \frac{1}{D}\right) \times 4 $.
- This equals the remaining work: $ \left(\frac{1}{15} + \frac{1}{D}\right) \times 4 = \frac{7}{15} $.
- Distribute the $4$: $ \frac{4}{15} + \frac{4}{D} = \frac{7}{15} $.
- Isolate the term with $D$: $ \frac{4}{D} = \frac{7}{15} - \frac{4}{15} $.
- $ \frac{4}{D} = \frac{3}{15} = \frac{1}{5} $.
- Solve for $D$: $ D = 4 \times 5 = 20 $.
Therefore, Deven can finish the work alone in $20\text{ days}$.
Similar Questions
A and B can complete a task together in 12 days, while B and C can finish it in 16 days. After A works on it for 5 days and B for 7 days, C takes the remaining 13 days to finish the work. How many days would it take for C to complete the work alone?
A is three times more efficient as a worker than B, which allows A to complete a job in 60 days less than B. If they work together, they can finish the job in:
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Important Questions from Time and Work
Mohan can do a piece of work in 10 days and Sohan in 15 days. They started working together, but after 3 days Mohan left the work . What time will Sohan take to finish the work?
A tank is filled in 8 hours by three taps A, B and C. The tap C is thrice as fast as B and B is twice as fast as A. How much time will pipe B alone take to fill the tank?
Had been one menless, then the number of days required to do a piece of work would have been one more. If the number of Man. Days required to complete the work is 56, how many workers were there?
A can do a piece of work in 16 hours, B and C can do it in 8 hours while A and C can do it 12 hours. How long will B alone take to do it?
- lf 12 men can do a work in 20 days, in how many days will the work be done by 15 men-
