This problem involves calculating the time A needs to complete the remaining work after B has worked for a certain period.
Calculating Work Rates
First, determine the fraction of the work each person completes per day:
- A's daily work rate = $\frac{1}{\text{A's total days}} = \frac{1}{5}$ of the work per day.
- B's daily work rate = $\frac{1}{\text{B's total days}} = \frac{1}{50}$ of the work per day.
Work Done by B
B worked alone for 10 days. Calculate the portion of the work B completed:
- Work done by B = B's rate $\times$ Time worked
- Work done by B = $\frac{1}{50} \times 10 = \frac{10}{50} = \frac{1}{5}$ of the total work.
Calculating Remaining Work
Determine the amount of work left to be done:
- Remaining Work = Total Work - Work done by B
- Remaining Work = $1 - \frac{1}{5} = \frac{4}{5}$ of the total work.
Time for A to Finish Work
Calculate how many days A needs to complete the remaining work using A's daily rate:
- Time = $\frac{\text{Remaining Work}}{\text{A's daily rate}}$
- Time = $\frac{4/5}{1/5}$
- Time = $\frac{4}{5} \times \frac{5}{1} = 4$ days.
Therefore, A can finish the remaining work alone in 4 days.
Important Questions from Time & Work (Notes)
- A fresh water tap fills a fish tank in 40 minutes. The same tank is filled by a salt water tap in 120 minutes. If both the taps are open, how many minutes will it take to fill the tank?
- A completes $\frac{7}{10}$ of a work in 15 days and then he completes the remaining work with the help of B in 5 days. In how many days can A and B together complete the entire work?
Aman can do 50% of the job in 16 days, and Bhanu can do 25% of the job in 24 days. In how many days can they do $\frac{1}{4}^{th}$ of the job working together ?
- Three workers A, B, C can finish a job in 10, 15, and 20 hours respectively. A and B start; after 2 hours, C joins and they finish the remaining work in t more hours. What is the value of t? (Rounded off to the nearest integer.)
- X can finish a job in $141$ days. He worked for $57$ days alone and the remaining work was completed by Y, in $84$ days. How many days would both together take to complete the entire job?
