Question : One man and one woman together can complete a piece of work in 8 days. A man alone can complete the work in 10 days. In how many days can one woman alone complete the work?
Option 1: $\frac{140}{9}$ days
Option 2: $30$ days
Option 3: $40$ days
Option 4: $42$ days
Correct Answer: $40$ days
Solution :
Given,
The time taken by one man and one woman to complete the work = 8 days
Time taken by a man to complete the work = 10 days
⇒ one man's 1 day's work = $\frac{1}{10}$
Work done by one man and one woman in 1 day = $\frac{1}{8}$
⇒ In one day work done by one woman = $\frac{1}{8}-\frac{1}{10}=\frac{10-8}{80}=\frac{2}{80}=\frac{1}{40}$
$\therefore$ Time taken by one woman to complete the work = 40 days
Hence, the correct answer is $40$ days.
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