Question:hard

Anil can paint a house in 60 days while Bimal can paint it in 84 days. Anil starts painting and after 10 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, in INR, proportionate to the work done by him, is

Updated On: Jan 15, 2026
  • 9000
  • 9100
  • 9200
  • 9150
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The Correct Option is B

Solution and Explanation

To ascertain Charu's payment allocation, we must first quantify the contribution of each individual.

1. Establish individual daily work rates:

  • Anil's rate: Anil completes the task in 60 days, equating to a daily rate of \( \frac{1}{60} \).
  • Bimal's rate: Bimal completes the task in 84 days, equating to a daily rate of \( \frac{1}{84} \).

2. Quantify Anil's work over the initial 10 days:

Anil's work in 10 days = \( 10 \times \frac{1}{60} = \frac{1}{6} \).

3. Determine the combined work rate and Charu's individual rate:

  • Anil and Bimal's combined rate: \[ \frac{1}{60} + \frac{1}{84} = \frac{7}{420} + \frac{5}{420} = \frac{12}{420} = \frac{1}{35} \]
  • Charu's rate: Let \( \frac{1}{c} \) represent Charu's daily work rate. Combined, they finish the remaining \( \frac{5}{6} \) of the work in 14 days: \[ 14 \left( \frac{1}{60} + \frac{1}{84} + \frac{1}{c} \right) = \frac{5}{6} \]

4. Calculate Charu's work rate:

  • From the equation: \[ 14 \left( \frac{1}{35} + \frac{1}{c} \right) = \frac{5}{6} \] Simplified expression: \[ \frac{14}{35} + \frac{14}{c} = \frac{5}{6} \]
  • Solve for \( \frac{14}{c} \): \[ \frac{14}{c} = \frac{5}{6} - \frac{2}{5} \]
  • Utilize a common denominator: \[ \frac{5}{6} = \frac{25}{30}, \quad \frac{2}{5} = \frac{12}{30} \] Resulting subtraction: \[ \frac{25}{30} - \frac{12}{30} = \frac{13}{30} \]
  • Derive \( c \): \[ \frac{14}{c} = \frac{13}{30} \quad \Rightarrow \quad c = \frac{14 \times 30}{13} = \frac{420}{13} \]

5. Calculate Charu's work output and corresponding payment:

  • Charu's total work contribution: \[ 14 \times \frac{1}{c} = 14 \times \frac{13}{420} = \frac{182}{420} = \frac{91}{210} = \frac{13}{30} \]
  • Proportion of total payment (₹21000): \[ 21000 \times \frac{13}{30} = ₹9100 \]

Final Answer:

Charu is entitled to ₹9,100 of the payment.

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Questions Asked in CAT exam

The passage given below is followed by four summaries. Choose the option that best captures the essence of the passage.
In the dynamic realm of creativity, artists often find themselves at the crossroads between drawing inspiration from diverse cultures and inadvertently crossing into the territory of cultural appropriation. Inspiration is the lifeblood of creativity, driving artists to create works that resonate across borders. In a globalized era of the modern world, artists draw from a vast array of cultural influences. When approached respectfully, inspiration becomes a bridge, fostering understanding and appreciation of cultural diversity. However, the line between inspiration and cultural appropriation can be thin and easily blurred.
Cultural appropriation occurs when elements from a particular culture are borrowed without proper understanding, respect, or acknowledgment. This leads to the commodification of sacred symbols, the reinforcement of stereotypes, and the erasure of the cultural context from which these elements originated. It is essential to recognize that the impact of cultural appropriation extends beyond the realm of artistic expression, influencing societal perceptions and perpetuating power imbalances.
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