Question

P and Q can complete a piece of work in 28 days and 35 days, respectively. P begins to do the work and they work alternatively one at a time for one day each. In how many days will the whole work be completed?

• A. 31
• B. 27
• C. 18
• D. 21

Answer 1

Answer:

A. 31

P’s 1-day work = ( \frac{1}{28} )
Q’s 1-day work = ( \frac{1}{35} )

They work alternatively, starting with P.

Work done in 2 days (P + Q):

$\frac{1}{28} + \frac{1}{35}$
$= \frac{5 + 4}{140}$
$= \frac{9}{140}$

Total work:

In 2 days → $<b>( \frac{9}{140} )</b> work is done.$

So, in 30 days (15 cycles):

$15 \times \frac{9}{140} = \frac{135}{140}$

Remaining work:

$1 - \frac{135}{140} = \frac{5}{140} = \frac{1}{28}$

Day 31:

Next turn is P, and P can complete ( \frac{1}{28} ) in 1 day.

So remaining work is finished on this day.

Final Answer:

31 days