X, Y, and Z can complete a project in 20, 40, and 60 days respectively. X works every day, while Y and Z join X every third day. How long will it take to finish the project? 7

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1. Rates: X = $1/20$, Y = $1/40$, Z = $1/60$.

2. In each 3-day cycle: Day1 X = $1/20$, Day2 X = $1/20$, Day3 X+Y+Z = $1/20+1/40+1/60=11/120$. Total in 3 days = $2	imes	frac{1}{20}+	frac{11}{120}=	frac{23}{120}$.

3. After 15 days (5 cycles) work done = $5	imes	frac{23}{120}=	frac{115}{120}$. Remaining = $1-	frac{115}{120}=	frac{5}{120}=	frac{1}{24}$.

4. On day 16 only X works with rate $1/20$. Time to finish = $(1/24)\div(1/20)=	frac{5}{6}$ day. Total = $15+	frac{5}{6}=15	frac{5}{6}$ days. Hence option **(b)**.

FINAL_ANSWER: b

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