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Question 13 : Amal can complete a job in 10 days and Bimal can complete it in 8 days. Amal, Bimal and Kamal together complete the job in 4 days and are paid a total amount of Rs 1000 as remuneration. If this amount is shared by them in proportion to their work, then Kamal's share, in rupees, is

  1. 100
  2. 200
  3. 300
  4. 400

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Explanatory Answer

Method of solving this CAT Question from Work and Time

Given that Amal can complete a job in 10 days ⟹ Rate = \\frac{1}{10})
Bimal can complete it in 8 days ⟹ Rate = \\frac{1}{8})
Amal, Bimal and Kamal together complete the job in 4 days ⟹ Rate = \\frac{1}{4})
Kamal's rate of doing work is,
Amal + Bimal + Kamal = \\frac{1}{4})
⟹ \\frac{1}{10}) + \\frac{1}{8}) + Kamal = \\frac{1}{4})
⟹ Kamal = \\frac{1}{4}) - \\frac{1}{8}) − \\frac{1}{10})
⟹ Kamal = \\frac{10}{40}) - \\frac{5}{40}) − \\frac{4}{40})
Kamal’s rate of doing work = \\frac{1}{40})
Kamal would have taken 40 days to complete the entire task.
Amal : Bimal : Kamal = \\frac{1}{10}) : \\frac{1}{8}) : \\frac{1}{40}) = 4 : 5 : 1
Total amount of Rs.1000 is paid as remuneration
Amal : Bimal : Kamal = \\frac{4}{10}) : \\frac{5}{10}) : \\frac{1}{10})
Kamal’s share = \\frac{1}{10}) × 1000 = Rs.100

The question is "Amal can complete a job in 10 days and Bimal can complete it in 8 days. Amal, Bimal and Kamal together complete the job in 4 days and are paid a total amount of Rs 1000 as remuneration. If this amount is shared by them in proportion to their work, then Kamal's share, in rupees, is"

Hence, the answer is Rs.100

Choice A is the correct answer

 

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