Question
Download Solution PDFRavi and Raju can do a piece of work separately in 12 days and 20 days, respectively. If they work alternate days, with Ravi starting first, then in how many days will they complete the entire work?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Time taken by Ravi = 12 days
Time taken by Raju = 20 days
Ravi starts first, working on alternate days.
Formula Used:
Total Work = LCM of time taken by individuals
Efficiency = Total Work / Time taken
Calculation:
Total Work = LCM(12, 20) = 60 units
Efficiency of Ravi = Total Work / Time taken by Ravi = 60 / 12 = 5 units/day
Efficiency of Raju = Total Work / Time taken by Raju = 60 / 20 = 3 units/day
Work done in the first 2 days (Ravi then Raju) = Efficiency of Ravi + Efficiency of Raju = 5 + 3 = 8 units
Number of 2-day cycles to complete most of the work = Total Work / Work done in 2 days ≈ 60 / 8 = 7.5 cycles
Work done in 7 cycles (14 days) = 7 × 8 = 56 units
Remaining work = Total Work - Work done in 14 days = 60 - 56 = 4 units
On the 15th day, it's Ravi's turn. Ravi can do 5 units of work in a day.
Since only 4 units of work are remaining,
Time taken by Ravi to complete it = 4/5 days
Total days taken = 14 (for 7 cycles) + 4/5 (on the 15th day by Ravi) = 14.8 days.
They will complete the entire work in 14.8 days.
Last updated on Jun 11, 2024
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