Question

A. B and C together can do a piece of work in $40$ days. After working with B and C for $16$ days, A leaves and then B and C complete the remaining work in $40$ days more. A alone could do the work in

• A. $80$ days
• B. $90$ days
• C. $100$ days
• D. $120$ days

Answer 1

Answer: (C)

$100$ days

Let the total work be $80$ units. [LCM of $40$ and $16$]
(A + B + C) do = $\frac{80}{40}$ = $2$ units/day
(A + B + C) work for $16$ days, complete $16\times$ 2 = $32$ units of work
Work left is $80-32=48$ units.
B and C do = $\frac{48}{40}$ =$\frac{12}{10}$ = $1.2$ units/day
A does = $2-1.2$ units = $0.8$ unit/day
A will complete the work in = $\frac{80}{0.8}$ = $100$ days