A can complete $\frac{1}{3}$ of a work in 5 days and B, $\frac{2}{5}$ of the work in 10 days, In how many days both A and B together can complete the work?

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$\frac{29}{4}$ days

10 days

$\frac{75}{8}$ days

$\frac{44}{5}$ days

answer is B.

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Detailed Solution

The part of the work done by A in one day is $\frac{1}{3} \cdot \frac{1}{5} = \frac{1}{15}$

The part of the work done by $B$ in one day is $\frac{2}{5} \cdot \frac{1}{10} = \frac{1}{25}$

The part of the work done by both A and B together is $\frac{1}{15} + \frac{1}{25} = \frac{5 + 3}{75} = \frac{8}{75}$

The number of days that both together A and B together to complete the work is $\frac{75}{8}$ days.

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