'R' can independently complete a task in 36 days, whereas 'S' can accomplish 40% of the same work within 16 days. 'S' starts the task solo and withdraws after 10 days. Subsequently, the remaining work is undertaken collaboratively by 'R' and 'M,' culminating in its completion in 12 days. Calculate the duration required for 'S' and 'M' to jointly execute the same task.
ATQ, S alone can do the work in 16/0.4 = 40 days Let, total work be LCM of 36 and 40 = 360 units Units of work done by R in a day = 360/36 = 10 Units of work done by S in a day = 360/40 = 9 Units of work done by S on 10 days = 9 × 10 = 90 Remaining work = 360 – 90 = 270 units Let, M can do ‘m’ units work per day So, 270/(10 + m) = 12 270 = 120 + 12m 12m = 150 m = 12.5 Required time taken = 360/(9 + 12.5) = 720/43 days
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