Question

A, B, and C are capable of completing a job in 30, 45, and 90 days, respectively. A works every day, while B and C join A every fifth day. How long will it take to finish the task?

• A. 25 days
• B. 18 days
• C. 13 days
• D. 17 days

Answer 1

Answer:

A. 25 days

Work done per day:

• A’s one day work $(= \frac{1}{30})$

• B’s one day work $(= \frac{1}{45})$

• C’s one day work $(= \frac{1}{90})$

On every 5th day, all three work together.

Work done by A alone for 4 days:

• $4\times\frac{1}{30}=\frac{2}{15}$

Work done on the 5th day by A, B, and C together:

$\frac{1}{30}+\frac{1}{45}+\frac{1}{90}$

$LCM (= 90)$

$=\frac{3+2+1}{90}=\frac{6}{90}=\frac{1}{15}$

Total work in 5 days:

• $\frac{2}{15}+\frac{1}{15}=\frac{3}{15}=\frac{1}{5}$

So,$(\frac{1}{5})$ of the work is completed every 5 days.

Hence total time:

$5 \times 5 = 25 \text{ days}$

Therefore, the task will be completed in 25 days.