Question

Q43.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 be done if A is assisted by B and C on alternate days?

• A. (a) 7 days
• B. (b) 8 days
• C. (c) 9 days
• D. (d) 10 days

Answer 1

The correct option is B

(b) 8 days

Work done by A in one day = $\frac{1}{11}$

Work done by B in one day = $\frac{1}{20}$

Work done by C in one day = $\frac{1}{55}$

Work done by (A + B) in one day = $\frac{1}{11}+\frac{1}{20}=\frac{31}{220}$

Work done by (A + C) in one day = $\frac{1}{20}+\frac{1}{55}=\frac{6}{55}$

Work done by (2A + B +C) in 2 days

$=\frac{31}{220}+\frac{6}{55}=\frac{55}{220}=\frac{1}{4}$

Work done by (2A + B + C) in 1 day = $\frac{1}{8}$

So, work will be completed in 8 days