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(D) Let the work done in one day by $A, B,$ and $C$ be $a, b,$ and $c$ respectively.Given:$a + b = 1/20$ $(i)$$b + c = 1/30$ (ii)$a + c = 1/40$ (iii)A

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$1:5$

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(D) Let the work done in one day by $A, B,$ and $C$ be $a, b,$ and $c$ respectively.Given:$a + b = 1/20$ $(i)$$b + c = 1/30$ (ii)$a + c = 1/40$ (iii)Adding $(i)$,(ii),and (iii),we get:$2(a + b + c) = 1/20 + 1/30 + 1/40 = (6 + 4 + 3) / 120 = 13/120$$a + b + c = 13/240$To find $A$'s one day work $(a)$: $a = (a + b + c) - (b + c) = 13/240 - 1/30 = (13 - 8) / 240 = 5/240 = 1/48$.So,$A$ takes $48$ days to complete the task alone.To find $C$'s one day work $(c)$: $c = (a + b + c) - (a + b) = 13/240 - 1/20 = (13 - 12) / 240 = 1/240$.So,$C$ takes $240$ days to complete the task alone.The ratio of days taken by $A$ to $C$ is $48 : 240 = 1 : 5$.

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