Question

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

• A. 9000
• B. 9100
• C. 9200
• D. 9150

Answer 1

The Correct Option is B

We need to determine Charu's share of the payment. To do this, we first calculate how much work each person contributed.

1. Calculate the daily work rate of Anil, Bimal, and Charu:

• Anil's work rate: Since Anil can finish the work in 60 days, his daily work rate is \( \frac{1}{60} \).
• Bimal's work rate: Bimal can finish it in 84 days, so his daily work rate is \( \frac{1}{84} \).

2. Calculate the work done by Anil in the first 10 days:

Work done by Anil in 10 days = \( 10 \times \frac{1}{60} = \frac{1}{6} \).

3. Calculate the work rate of Anil, Bimal, and Charu working together:

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

4. Determine Charu's work rate:

• From the equation: \[ 14 \left( \frac{1}{35} + \frac{1}{c} \right) = \frac{5}{6} \] Simplifying: \[ \frac{14}{35} + \frac{14}{c} = \frac{5}{6} \]
• We now solve for \( \frac{14}{c} \): \[ \frac{14}{c} = \frac{5}{6} - \frac{2}{5} \]
• Finding a common denominator: \[ \frac{5}{6} = \frac{25}{30}, \quad \frac{2}{5} = \frac{12}{30} \] Thus: \[ \frac{25}{30} - \frac{12}{30} = \frac{13}{30} \]
• Therefore: \[ \frac{14}{c} = \frac{13}{30} \quad \Rightarrow \quad c = \frac{14 \times 30}{13} = \frac{420}{13} \]

5. Calculate Charu's share of the work and payment:

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

Final Answer:

Charu’s share of the payment is ₹9,100.

Answer 2

Let the entire task be denoted by \( W \). Anil worked for 24 days and completed \( 0.4W \) in those 24 days. Bimal and Charu worked for a total of 14 days.

Step 1: Anil's work rate

Anil completes \( 0.4W \) in 24 days, so his rate of work is:

\[ \frac{0.4W}{24} \quad \Rightarrow \quad \text{Anil completes } \frac{W}{60} \text{ per day.} \]

Step 2: Bimal's work rate

Bimal completes \( W \) in 84 days, so his rate of work is:

\[ \frac{W}{84} \quad \Rightarrow \quad \text{Bimal completes } \frac{W}{84} \text{ per day.} \] After 14 days, Bimal will have completed: \[ \frac{W}{6} \]

Step 3: Charu's work completion

After Bimal completes \( \frac{W}{6} \) and Anil completes \( \frac{4W}{10} \) (since \( \frac{0.4W}{24} \times 14 \) for 14 days), Charu must complete the rest. The remaining work is: \[ W - \frac{W}{6} - \frac{4W}{10} = \frac{26W}{30} = \frac{13W}{15} \] So, Charu completes \( \frac{13W}{30} \).

Step 4: Charu's share

The total amount Charu earns based on the total payment of \( 21,000 \) is: \[ \frac{13}{30} \times 21000 = 9100 \]

Final Answer:

Charu’s proportion of the total payment is ₹9,100.