Ratan takes 5 days to complete a certain job and shankar takes 8 days to do the same job. If both of them work together, how long will they take to complete the work ?

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Solution

Since, Ratan takes 5 days to complete the given work
$∴$ Ratan finishes $\frac{1}{5}$ part in 1 day.
Similarly, Shankar takes 8 days to complete the work. Therefore, Shankar finishes $\frac{1}{8}$ part in 1 day.
$∴$ In a day, they together will finish = $\frac{1}{5} + \frac{1}{8} = \frac{8 + 5}{40} = \frac{13}{40}$
i.e., $\frac{13}{40}$ part of the work.
So, they both will take $\frac{40}{13}$ days $3 \frac{1}{13}$ days to complete the work. Hence, the complete work will be finished by them together in $3 \frac{1}{13}$ days

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