A can do a job in 3 days less time than B. A works at it alone for 4 days and then B takes over and completes it. If altogether 14 days were required to finish the job, how many days would each of them take alone to finish it? Choose one:
A) 17 days, 20 days	B) 12 days, 15 days	C) 13 days, 16 days	D) 14 days, 11 days	E) None of these
Let B can finish the work in x days.   Then A can finish the work in (x – 3) days.   B’s one day’s work = 1⁄xth work.   A’s one day’s work = 1⁄(x - 3)th work.   A’s 4 days’ work = 4⁄(x - 3)th work.   Remaining work = 1 - 4⁄(x - 3) = x−7 /x−3   The remaining work done by B in 14 – 4 = 10 days.   Now, in 10 days, work done by B = x−7/x−3th work.   ∴ in 1 day, work done by B = 110(x−7/x−3) th work.   and 1/10(x−7/x−3)=1/x   ⇒ x = 15 days   ∴ 12 days, 15 days → 15 days and A → 12 days   Answer 12 days, 15 days
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A can do a job in 3 days less time than B. A works at it alone for 4 days and then B takes over and completes it. If altogether 14 days were required to finish the job, how many days would each of them take alone to finish it?