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?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 31.
LCM of 28 and 35 ⇒ 140
P’s 1 day work ⇒ 140 ÷ 28 = 5 units
Q’s 1 day work ⇒ 140 ÷ 35 = 4 units
Work done in 2 days ⇒ 5 + 4 = 9 units
15 × 2 days = 9 × 15 = 135 unit
Remaining work done by P = 5 unit = 1 day
total time = 30 + 1 = 31 days