Question
Download Solution PDFA, B and C can finish a work in 20, 25 and 30 days, respectively. They start working together but B quits after working for 3 days. In how many days from the start shall the work be completed ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFThe Correct answer is Option 3.
Key PointsTo solve the problem, we need to calculate the work done by A, B, and C together in the first 3 days, and then determine how much work remains and how long it will take for A and C to finish the remaining work.
Work rate of A:
⇒ A can finish the work in 20 days.
Work rate of A = 1/20 of the work per day.
Work rate of B:
⇒ B can finish the work in 25 days.
Work rate of B = 1/25 of the work per day.
Work rate of C:
⇒ C can finish the work in 30 days.
Work rate of C = 1/30 of the work per day.
⇒ The combined work rate of A, B, and C when they work together is: Combined rate = 1/20 + 1/25 + 1/30
⇒ To add these fractions, we find a common denominator (which is 300): 1/20 = 15/300, 1/25 = 12/300, 1/30 = 10/300
⇒ So, Combined rate = 15/300 + 12/300 + 10/300 = 37/300 of the work per day
⇒ In the first 3 days, A, B, and C together complete: Work done in 3 days = Combined rate × Time = (37/300) × 3 = 111/300 of the work
⇒The total work is 1 (whole work), so the remaining work after 3 days is: Remaining work = 1 - 111/300 = 189/300 = 63/100
⇒ Now, A and C will continue to work together. The combined work rate of A and C is: Combined rate of A and C = 1/20 + 1/30
⇒ Finding a common denominator (which is 60): 1/20 = 3/60, 1/30 = 2/60
⇒ So, Combined rate of A and C = 3/60 + 2/60 = 5/60 = 1/12 of the work per day
⇒ To find the time (T) it takes for A and C to finish the remaining 63/100 of the work at the rate of 1/12 of the work per day: T = Remaining work / Combined rate of A and C = (63/100) / (1/12) = (63/100) × 12 = 756/100 = 7.56 days
⇒ The total time from the start is the initial 3 days plus the time taken by A and C to finish the remaining work: Total time = 3 + 7.56 = 10.56 days
Thus, the total time from the start when the work is completed is:
10.56 days = 264/25 days
The correct answer is: 3) 264/25 days
Last updated on Jun 14, 2025
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