Question

Please answer legit with explanation:

A, B and C can do a piece of work together in 10, 15 and 20 days respectively. They began their work together but A left the work after 2 days, and B left the work after 3 days. In how many days will C alone would finish the work?

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Answer 1

$\frac{1}{10} + \frac{1}{15} + \frac{1}{20} = \frac{6 + 4 + 3}{60} \\ work \: done \: in \: one \: day = \frac{13}{16} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: in \: two \: day \: = \frac{13}{60} \times 2 \\ \: \: \: \: = \frac{13}{30} \\ work \: remain \: 1 - \frac{13}{30} = \frac{17}{30}$
A left the the work B and C do the work together for three days
$\frac{1}{15} + \frac{1}{20} \\ \frac{4 + 3}{60} = \frac{7}{60} \\ \frac{7}{60} \times 3 = \frac{7}{20} \\ the \: work \: done \: by \: b \: and \: c \: = \frac{7}{20} \\ the \: work \: remain \: = \frac{17}{30} - \frac{7}{20} \\ \frac{34 - 21}{60} = \frac{13}{60}$
the C can complete the work
$20 \times \frac{13}{60} \\ \frac{13}{3} = 4 \frac{1}{3}$
the C could complete the work in above mentioned answer .