Work Rate Problem: Calculating C's Task Time
This solution outlines the steps to find how long C alone takes to complete a task, given the work rates of A and B and their combined effort.
Work Rates: A and B Individual Task Time
- A's daily rate: $\frac{1}{30}$ of the task.
- B's daily rate: $\frac{1}{40}$ of the task.
Combined Work Rate: A and B Together
The combined daily rate for A and B is:
$ \text{Rate}_{A+B} = \frac{1}{30} + \frac{1}{40} = \frac{4+3}{120} = \frac{7}{120} \text{ task/day} $
Work done by A and B in $10$ days:
$ \text{Work}_{A+B, 10 \text{ days}} = 10 \times \frac{7}{120} = \frac{7}{12} \text{ task} $
Remaining Work Calculation
The work remaining after A and B worked for 10 days is:
$ \text{Remaining Work} = 1 - \frac{7}{12} = \frac{5}{12} \text{ task} $
C completes this $\frac{5}{12}$ of the task in $5$ days.
C's Work Rate Determination
C's daily work rate is calculated as:
$ \text{Rate}_C = \frac{\text{Remaining Work}}{\text{Time}} = \frac{5/12 \text{ task}}{5 \text{ days}} = \frac{1}{12} \text{ task/day} $
C's Total Task Time Calculation
The total time C requires alone to complete the entire task (1 task) is:
$ \text{Time}_C = \frac{1}{\text{Rate}_C} = \frac{1}{1/12} = 12 \text{ days} $
Based on the calculations, C alone takes $12\text{ days}$ to complete the task.
Similar Questions
A and B can complete a task in 12 days together. A is 25% more efficient than B. What percentage of the work is done by A alone?
- The efficiency of A, B and C is 2 : 3 : 5. A alone can complete the work in 40 days. They all worked together for 5 days and then C left the work. In how many days can A and B together complete the remaining work?
20 women can do work in 16 days. 10 men can complete the same work in 12 days. What is the ratio between the efficiency of a man and a woman?
- Sameer can complete a work in 16 days. In how many days will the work be completed by Ajay, if his efficiency is 60% more than that of Sameer?
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?
