QUESTION

CSAT

Medium

Maths

Prelims 2016

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 wouldRam take to complete the entire job alone?

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Explanation

Let Ram's rate of working be R (fraction of the job completed per day). Let Shyam's rate of working be S (fraction of the job completed per day).

Together, Ram and Shyam work for 4 days to complete 60% of the job: 4(R+S)=0.604(R + S) = 0.60 So, R+S=0.60/4=0.15R + S = 0.60 / 4 = 0.15 (Equation 1)

After Ram leaves, Shyam works for 8 more days to complete the job: 8S=0.408S = 0.40 (since 60% is already completed, and 40% remains)

So, S=0.40/8=0.05S = 0.40 / 8 = 0.05 (Equation 2)

Now substitute the value of S in Equation 1: R+0.05=0.15R + 0.05 = 0.15 R=0.150.05=0.10R = 0.15 - 0.05 = 0.10

The time taken by Ram to complete the entire job alone is: Time = 1/R=1/0.10=101 / R = 1 / 0.10 = 10 days

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