A can do a piece of work in 15 days and B can do it in 24 days. If they do the work alternately, in how many days will they finish the work, provided that A begins the work?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 18.
A’s 1 day work = 1/15
B’s 1 day work = 1/24
Work in 2 days (A + B) = 1/15 + 1/24 = (8 + 5)/120 = 13/120
In 8 days (4 cycles), work done = 4 × 13/120 = 52/120 = 13/30
Remaining work = 1 – 13/30 = 17/30
Next day A works, so days needed = (17/30) ÷ (1/15) = (17/30) × 15 = 8.5 days
Total time = 8 + 0.5 = 8.5 days