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Farida alone can finish a tailoring order in 16 days and Gita alone in 24 days. They agree to work on alternate days, Farida taking the first day, Gita the second, and so on. On which day is the order finished?

Competition practiceTime & Work / Pipes
  • A18 days
  • B19.2 days
  • C19 days
  • D20 days

Step-by-Step Solution

Take the order as 48 units: Farida 3/day, Gita 2/day. A Farida-then-Gita pair of days yields 5 units. Nine such pairs — 18 days — give 45 units. Day 19 is Farida's, and her 3 units carry the total to exactly 48, so the order ends on day 19. 18 days stops at the last complete pair with 3 units still outstanding. 19.2 days averages the pair into a steady 2.5 units a day (48 ÷ 2.5), which ignores that the last day is worked by the faster of the two. 20 days rounds a further day on without checking that day 19 already closes the order.
Answer: C) 19 days

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