A can complete a work in 18 days, while B can complete it in 12 days. B worked on it for 4 days. How long will A take to finish the remaining work?
12 days
Understanding the Work and Time Problem
This problem involves calculating the time taken by individuals to complete a certain amount of work. We are given the time A and B take to complete the entire work individually and the duration B worked. We need to find out how long A will take to finish the remaining portion of the work.
Calculating Individual Work Rates
First, let's determine the amount of work A and B can complete in one day. This is called their daily work rate.
- A can complete the work in 18 days. So, A's daily work rate is the reciprocal of the total time taken by A.
- A's daily work rate $= \frac{1}{\text{Time taken by A}} = \frac{1}{18}$ of the work per day.
- B can complete the work in 12 days. So, B's daily work rate is the reciprocal of the total time taken by B.
- B's daily work rate $= \frac{1}{\text{Time taken by B}} = \frac{1}{12}$ of the work per day.
Work Done by B in 4 Days
B worked on the project for 4 days. To find the amount of work B completed, we multiply B's daily work rate by the number of days B worked.
- Work done by B in 4 days = B's daily work rate $\times$ Number of days B worked
- Work done by B $= \frac{1}{12} \times 4 = \frac{4}{12} = \frac{1}{3}$ of the total work.
Calculating the Remaining Work
The total work is considered as 1 whole unit. After B completed $\frac{1}{3}$ of the work, the remaining work is the total work minus the work done by B.
- Remaining work = Total work - Work done by B
- Remaining work $= 1 - \frac{1}{3} = \frac{3}{3} - \frac{1}{3} = \frac{3-1}{3} = \frac{2}{3}$ of the total work.
Time Taken by A to Finish Remaining Work
Now, A needs to complete the remaining $\frac{2}{3}$ of the work. We know A's daily work rate is $\frac{1}{18}$. To find the time A will take, we divide the remaining work by A's daily work rate.
- Time taken by A = $\frac{\text{Remaining work}}{\text{A's daily work rate}}$
- Time taken by A $= \frac{\frac{2}{3}}{\frac{1}{18}}$ days
- Time taken by A $= \frac{2}{3} \times \frac{18}{1} = \frac{2 \times 18}{3 \times 1} = \frac{36}{3}$ days
- Time taken by A $= 12$ days.
Therefore, A will take 12 days to finish the remaining work.
Summary of Calculations
| Task | Calculation | Result |
|---|---|---|
| A's Daily Rate | $1/18$ | $1/18$ |
| B's Daily Rate | $1/12$ | $1/12$ |
| Work Done by B (4 days) | $(1/12) \times 4$ | $1/3$ |
| Remaining Work | $1 - 1/3$ | $2/3$ |
| Time A Takes for Remaining Work | $(2/3) / (1/18)$ | 12 days |
Final Answer
A will take 12 days to finish the remaining work.
Revision Table: Work and Time Concepts
| Concept | Explanation | Formula |
|---|---|---|
| Work Rate | Amount of work done per unit of time (e.g., per day). | Work Rate $= \frac{\text{Total Work}}{\text{Time Taken}}$ |
| Total Work | Usually considered as 1 unit or the LCM of individual times. | $-$ |
| Time Taken | Total time needed to complete the work. | Time Taken $= \frac{\text{Total Work}}{\text{Work Rate}}$ |
| Work Done in 'n' days | Work rate multiplied by the number of days worked. | Work Done $= \text{Work Rate} \times \text{Number of Days}$ |
| Remaining Work | The portion of work left after some work is completed. | Remaining Work $= \text{Total Work} - \text{Work Done}$ |
Additional Information: Efficiency and Work
Efficiency is inversely proportional to the time taken to complete a work. If a person is more efficient, they take less time to finish the same amount of work. In this problem, B is more efficient than A because B takes 12 days while A takes 18 days to complete the same work.
When multiple people work together, their individual work rates are added up to find the combined work rate per day. For example, if A and B worked together, their combined daily work rate would be $\frac{1}{18} + \frac{1}{12}$.
Understanding these basic principles of work and time problems helps in solving various scenarios involving multiple individuals working for different durations or together.
Similar Questions
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?
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:
R, S and T can finish a work in 20, 15 and 10 days, respectively. R works on all days and S and T work on alternate days with T starting the work on the first day. In how many days is the work finished?
A can do \(1 \over 3\) of a piece of work in 32 days, B can do \(37{1 \over 2}\)% of the same work in 24 days, while C can do 60% of the same work in 48 days. B and C together started and worked for x days. After x days, B left the work and A joined C and both completed the remaining work in (x + 8) days. If the ratio of the work done by (B + C) together to the work done by (A + C) together is 9 ∶ 11, then what fraction of the same work can be completed by C alone in 3.5x days?
A group of college students had decided to complete a project in 10 days. As 2 students dropped out every day, the project got completed at the end of the 15th day. The number of students at the beginning of the project was:
A,B and C can do a piece of work in 30 days, 40 days and 50 days, respectively. Beginning with A, if A, B and C do the work alternatively then in how many days will the work be finished?
15 men can complete a work in 25 days, and 25 women can complete the same work in 40 days. If all 15 men and 25 women work together, in how many days will the work get completed?
Working 5 hours a day, A can complete a task in 8 days and working 6 hours a day, B can finish the same task in 10 days, working 8 hours a day, they can jointly complete the task in __________.
A can do 20% of a job in 7 days and B can do 25% of the job in 7 days if they worked alone. How much of the job (in percentage) can they complete in 7 days if they worked together?
Pratima and Diksha can complete a typing work separately in 10 hours and 15 hours, respectively. After typing for 4 hours alone, Pratima leaves the work. In how many hours will Diksha complete the remaining typing work?
Important Questions from Work Efficiency
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?
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?
