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)
- If 6 men and 8 boys can do a piece of work in 10 days and 26 men and 48 boys can do the same work in 2 days, then the time taken by 15 men and 20 boys to do the same work will be
- 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?
Three pipes A, B and C can fill a tank in $10$, $15$ and $20$ hours respectively. Pipe A was opened at $6$ AM, pipe B at $7$ AM and pipe C at $8$ AM. At what time was the tank completely filled, if pipe C needs a break of $1$ hour after remaining open for $3$ hours?
A tank has four pipes $P_1$, $P_2$, $P_3$ and $P_4$. The tank can be filled in $15$ minutes by pipes $P_1$, $P_2$, $P_3$ together. It can be filled in $20$ minutes by pipes $P_2$, $P_3$, $P_4$ together and it can be filled by pipes $P_1$, $P_4$ together in $30$ minutes. If all the pipes are opened together, then in how much time will the tank be filled?
$5$ men and $4$ women can earn ₹ $20000$ in $8$ days. $10$ men and $7$ women can earn ₹ $23,750$ in $5$ days. In how many days will $5$ men and $6$ women earn ₹ $12,000$?
