Multiple choice

Ram, Suraj and Rajesh are working on a short duration project. Ram alone can complete the project in 8 days, Suraj can complete the project in 10 days, while Rajesh can do it in 12 days. They start the work together, but after 2 days Ram leaves the work and the remaining project is completed by Suraj and Rajesh. How long (approximately) will the project take to get completed?

  1. 4 days

  2. 3 days

  3. 2 days

  4. 2.5 days

  5. None of these
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A Correct answer
Explanation

Rates: Ram=1/8, Suraj=1/10, Rajesh=1/12. Combined rate = (15+12+10)/120 = 37/120. In 2 days, they do 2 * (37/120) = 37/60. Remaining work = 23/60. Suraj and Rajesh rate = 1/10 + 1/12 = 11/60. Time to finish = (23/60) / (11/60) = 23/11 = 2.09 days. Total time = 2 + 2.09 = 4.09 days, which is approximately 4 days.

AI explanation

Using the least common multiple method, let the total project be 120 units of work, so Ram's daily work is 15 units, Suraj's is 12 units, and Rajesh's is 10 units. Together, their 1 day work is 37 units, and in 2 days they complete 74 units, leaving 46 units of work. Suraj and Rajesh's combined daily work is 22 units, so dividing the 46 remaining units by 22 gives approximately 2.09 days; adding this to the initial 2 days results in a total project duration of approximately 4 days.

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