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
- 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?
- 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?
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?
Important Questions from Work Efficiency
A and B together can complete a certain work in 20 days whereas B and C together can complete it in 24 days. If A is twice as good a workman as C, then in what time will B alone do 40% of the same work?
14 men can complete a work in 15 days. If 21 men are employed, then in how many days will they complete the same work?
A can do a certain work in 15 days, while B can do the same work in 21 days. If they work together, then in how many days will the same work be completed?
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:
Two men and 7 women can complete a work in 28 days whereas 6 men and 16 women can do the same work in 11 days. In how many days can 7 men complete the same work?
