A and B can complete a piece of work in 80 and 120 days respectively. They together start the work but A left after 20 days. After another 12 days C joined B and now they complete the work in 28 more days. In how many days C can complete the work, working

A and B can complete a piece of work in 80 and 120 days respectively. They together start the work but A left after 20 days. After another 12 days C joined B and now they complete the work in 28 more days. In how many days C can complete the work, working alone?
1). 100 days
2). 112 days
3). 120 days
4). 126 days

Solution

A did the work for $20$ days, B did the work for $(20 + 12 + 38) = 60$ days, C did the work for $28$ days.

Let $C$ alone can complete the work in $x$ days.

Fraction of work did by $A + Fraction$ of work did by $B + Fraction$ of work did by $C = 1$

Or $20/80+60/120+28/x=1$

Or $x=28×4 = 112$ days

$C$ alone can complete the work in $112$ days

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