Question
Download Solution PDFPrem can do a piece of work in 112 days. Ben can do this work in 90 days. Prem started the work alone. After how many days should Ben join him, so that the total work is finished in 56 days?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven
Prem's work time = 112 days
Ben's work time = 90 days
Total time to finish the work = 56 days
Concept:
In the scenario of combined work, (Total work) = (Work rate) × (Time), where work rate is the inverse of the time taken to finish the work alone.
Calculation:
⇒ Prem's work rate = 1/112 per day
⇒ Ben's work rate = 1/90 per day
⇒ Combined work rate = Prem's work rate + Ben's work rate = 1/112 + 1/90 = 1/56 per day
The total number of days Ben works be x
So, Prem works for 56 days and Ben works for x days to complete work
56/112 + x/90 = 1
⇒ 56 × 45 + 56x = 112 × 45
⇒ 56x + 6272 - 112x = 112 × 45 - 56 × 45
⇒ 56x = 56 × 45
⇒ x = 45
Ben join after 56 - 45 = 11 days
Hence, Ben should join Prem after 11 days.
Last updated on Jul 8, 2025
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