Ram can do a piece of work in 10 days and Anshu in 20 days. They work together, but 2 days before the completion of the work, Ram leaves and Anshu completes the work. In total how many days was the work completed?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 8 days
A person who finishes a job in \(n\) days does \(\frac{1}{n}\) of it in one day, and the one-day work of people working together is added. The last 2 days are Anshu’s alone, so that part is taken out first and the rest is done by both.
Ram’s one-day work \(=\frac{1}{10}\), Anshu’s \(=\frac{1}{20}\)
Together \(\displaystyle =\frac{1}{10}+\frac{1}{20}=\frac{3}{20}\) a day
Anshu alone in the last 2 days \(\displaystyle =2\times\frac{1}{20}=\frac{1}{10}\)
Work done by both \(\displaystyle =1-\frac{1}{10}=\frac{9}{10}\)
Days they work together \(\displaystyle =\frac{9}{10}\div\frac{3}{20}=\frac{9}{10}\times\frac{20}{3}=6\)
Total \(=6+2=8\) days
Shortcut: Anshu works on every day of the job and Ram on all but the last 2. Let the job take \(t\) days.
\(\displaystyle \frac{t-2}{10}+\frac{t}{20}=1\)
\(2(t-2)+t=20\), so \(3t=24\) and \(t=8\)