Question
A and B can complete a work in 12 days and 6 days, respectively. They started doing the work together but after 2 days, B had to leave, and A completed the remaining work alone. The remaining work was completed in ________ days.
The correct answer is
6
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.
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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?
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