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CAT 2021 Set-2 | Quantitative Aptitude | Question: 13

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Anil can paint a house in $60 \; \text{days}$ while Bimal can paint it in $84 \; \text{days}.$ Anil starts painting and after $10 \; \text{days},$ Bimal and Charu join him. Together, they complete the painting in $14$ more days. If they are paid a total of $₹ \; 21000$ for the job, then the share of Charu, $\text{in INR},$ proportionate to the work done by him, is

  1. $9150$
  2. $9100$
  3. $9000$
  4. $9200$
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Let’s draw the table, for better understanding.

$\begin{array} {llll} & \textbf{Anil} & \textbf{Bimal} & \textbf{Charu} \\ \text{Time:} & 60\;\text{days} & 84\;\text{days} & \\ \text{Total work:} & \text{LCM(60,84)} & = & 420\;\text{units} \\ \text{Efficiency:} & 7\;\text{units/day} & 5\;\text{units/day} & C\;\text{units/day}\end{array}$

Now, $ \underbrace{10 \times 7}_{\text{Anil 10 days work}} + \underbrace{14 \times 7}_{\text{Anil 14 days work}} + \underbrace{14 \times 5}_{\text{Bimal 14 days work }} + \underbrace{14C}_{\text{Charu 14 days work}} = 420 $

 $ \Rightarrow 70 + 98 + 70 + 14c = 420 $

$ \Rightarrow 14c = 420 – 238 $

$ \Rightarrow \boxed{ 14c = 182 \; \text{units}}$

$\therefore$ The share of Charu $ = \frac{182}{420} \times 21000  = ₹ \; 9100.$

Correct Answer $: \text{B}$
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