Ram, Ravi and Ratan can alone finish an assignment in 9 days, 12 days and 15 days respectively. They decide to complete a work by working in turns. Ram works alone on Monday, Ravi does the work alone on Tuesday, followed by Ratan working alone on Wednesday & so on. What proportion of the complete work is done by Ravi?
Explanation:
Let the total work be 180 units (LCM of 9, 12 and 15) and let Ram, Ravi and Ratan do a, b and c units of work per day.
∴ a = 180/9 = 20; b = 180/12 = 15 and c
= 180/15 = 12
Ram works alone on Monday, Ravi works alone on Tuesday and Ratan works alone on Wednesday.
∴ Work done in three days = a + b + c
= 20 + 15 + 12 = 47
∴ Work done in nine days = 3(47)
= 141 units
On the 10th day, Ram does 20 units, thereby taking the completed total work to 141 + 20 = 161 units.
On the 11th day, Ravi does 15 units, hence, taking the completed total work to 176 units.
The work gets completed on the 12th day.
Hence, Ravi has done work equivalent to four days when the work is completed.
∴ Ravi’s total work = 4(15) = 60 units
∴ Required proportion = 60/180 = 1/3
Hence, option (c).
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