Work Rate Analysis for A and B
First, determine the daily work rate for both individuals.
- A completes the work in 12 days, so A's daily rate is $ \frac{1}{12} $.
- B completes the work in 6 days, so B's daily rate is $ \frac{1}{6} $.
Combined Work and Remaining Work
Calculate the work done when they work together and the remaining portion.
- Their combined daily rate is $ \frac{1}{12} + \frac{1}{6} = \frac{1}{12} + \frac{2}{12} = \frac{3}{12} = \frac{1}{4} $ of the work.
- In the 2 days they worked together, they completed $ \frac{1}{4} \times 2 = \frac{1}{2} $ of the work.
- The remaining work is $ 1 - \frac{1}{2} = \frac{1}{2} $.
A Completes Remaining Work
Determine the time A needs to finish the rest of the work alone.
- A's daily rate is $ \frac{1}{12} $.
- Time for A to complete the remaining $ \frac{1}{2} $ work = $ \frac{1/2}{1/12} $.
- Calculation: $ \frac{1}{2} \times 12 = 6 $ days.
A completed the remaining work in 6 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 ₹ $12,000$?
