Ram and Shyam work on a job together for four days and complete 60% of it. Ram takes leave then and Shyam works for eight more days to complete the job. How long would Ram take to complete the entire job alone?

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Submitted by examrobotsa on

Q: 147 (IAS/1994)
Ram and Shyam work on a job together for four days and complete 60% of it. Ram takes leave then and Shyam works for eight more days to complete the job. How long would Ram take to complete the entire job alone?

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,10,12,5,3,10,4

keywords: 

{'shyam': [0, 1, 0, 0], 'days': [0, 0, 2, 0], 'more days': [0, 1, 0, 0], 'ram': [0, 1, 0, 1], 'job': [0, 1, 2, 1], 'entire job': [0, 1, 0, 0]}

In this scenario, Ram and Shyam collectively work for four days and manage to complete 60% of the job together. If we assume Ram alone could complete the job in `x` number of days, then in 4 days Ram would finish 4/x of the work. Shyam, left to complete the project, takes eight more days. Now, if Shyam alone could do the job in `y` days, then in total (4 + 8 = 12) days, Shyam would complete 12/y of the job. Since together they have completed 100% of the job, this can be written in equation form: 4/x + 12/y = 1. Since we know from the problem that Ram and Shyam completed 60% in 4 days, we can denote this as 4/x + 4/y = 0.6. Solving these equations, we find x is equal to 10. So, option 3 - "10 days" is the number of days Ram would take to complete the entire job alone.