A can lay railway track between two given stations in 16 days and B can do the sam job in 12 days with the help of ‘C’ then did the job in 4 days only then ‘C’ alone do the job in

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10 days

$9 \frac{1}{5}$ days

$9 \frac{3}{5}$ days

$9 \frac{2}{5}$ days

answer is C.

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Detailed Solution

$(A + B + C)$ 1 days work $= \frac{1}{4}$

A’s one day work $= \frac{1}{16}$

B’s one day work $= \frac{1}{12}$

$∴$ C’s one day work $= \frac{1}{4} - (\frac{1}{16} + \frac{1}{12})$

$= \frac{1}{4} - (\frac{3 + 4}{48})$

$= \frac{1}{4} - \frac{7}{48}$

$= \frac{5}{48}$

$∴$ ‘C’ alone can do the work

$= \frac{48}{5} = 9 \frac{3}{5}$ days

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