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CAT 2017 Set-2 | Question: 79

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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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$\begin{array}{lccc}  & \text{Amal} & \text{Bimal} & \text{(Amal+Bimal+Kamal)} \\ \text{Time:} & 10\;\text{days} & 8\;\text{days} & 4\;\text{days}\\ \text{Total work:} & \text{LCM(10,8,4)} & = 40\; \text{units} & \\ \text{Efficiency:} & 4 \;\text{unit/day} & 5\;\text{unit/day} & 10\;\text{unit/day}  \end{array}$

Efficiency of $\text{Amal + Bimal + Kamal} = 10$

$\Rightarrow 4 + 5 + \text{Kamal} = 10$

$\Rightarrow$  Efficiency of Kamal $ = 10-9 = 1$

Amal, Bimal and Kamal together complete the job in $4$ days and are paid a total amount of $\text{Rs}\; 1000$ as remuneration.

  • $10 \longrightarrow \text{Rs}\; 1000$
  • $1 \longrightarrow \text{Rs}\; 100$

$\therefore$ The Kamal’s share in rupees is $100.$

Correct Answer $:\text{A}$

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