Ramos, James, Cristiano and Modric can complete their physical assignment in 5, 10, 15 and 20 days. If Ramos and Modric works together for the first day and James and Cristiano together work for second day, they work in the same manner in coming days. How many days will be taken to complete the whole work?
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$\( \frac{14}{3} \) days$
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$\( \frac{22}{3} \) days$
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$\( \frac{10}{3} \) days$
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$\( \frac{16}{3} \) days$
A
Correct answer
Explanation
Individual rates: Ramos = 1/5 per day, James = 1/10 per day, Cristiano = 1/15 per day, Modric = 1/20 per day. Day 1 (Ramos + Modric): 1/5 + 1/20 = 5/20 = 1/4. Day 2 (James + Cristiano): 1/10 + 1/15 = 5/30 = 1/6. Two-day cycle completes 1/4 + 1/6 = 5/12 of work. After 4 days (2 cycles): 10/12 = 5/6 done. Day 5: 5/6 + 1/4 = 10/12 + 3/12 = 13/12 > 1, so work completes on day 5. Fraction of day 5 needed: 1 - 5/6 = 1/6, which takes (1/6)/(1/4) = 2/3 of day 5. Total days = 4 + 2/3 = 14/3 days.