Question

A, B and C can do a piece of work in 11 days, 20 days and 55 days respectively, working alone. How soon can the work he done if A is assisted by B and C on alternate days?

• A. 7 days
• B. 8 days
• C. 9 days
• D. 10 days

Answer 1

The correct option is B 8 days

Let the total work be 220 units (LCM of 11, 20 & 55).
A does =$\frac{220}{11}$ = 20 units / day
B does = $\frac{220}{20}$ = 11 units / day
C does =$\frac{220}{55}$=4 untis /day
according to the question,
(A + B) + (A + C) + (A + B) + (A + C) + .........
(20 + 11) +(20 + 4) + (20 + 11) + (20 + 4) +.
In 2 days, work get completed = 55 units.
55 units of work completed in 2 days.
220 units of work completed in
= $\frac{2}{55}\times 220=2\times 4$ = 8days.