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

Anil can paint a house in 60 days. So, he can do \(\frac{1}{60}\) of work per day.

Bimal can paint it in 84 days. So, he can do \(\frac{1}{84}\) of work per day.

Let’s assume charu can paint it in ‘c’ days. So, he can do \(\frac{1}{c}\) of work per day.
Anil alone does the work for 10 days. So, the work completed is 1616
The remaining work is \(\frac{5}{6}.\)
After that, for 14 days they worked together.

\(\frac{14}{60}+\frac{14}{84}+\frac{14}{c}=\frac{5}{6}.\)

\(\frac{1}{c}= \frac{13}{30}×14\)
Charu does his work for 14 days. So, the total work done by charu is \(\frac{13}{30}\)

The amount earned by charu = \(\frac{13}{30}\times 21000 = Rs 9100\)

Answer 2

Allow the entire task to be W 
Anil worked for 24 days now. 
For a total of fourteen days, Bimal and Charu worked. 
Now that Anil has achieved W in 60 days, he has completed 0.4W in 24 days. 
In 84 days, Bimal finishes W.
Therefore, after 14 days, Bimal finishes = \(\frac{W}{6}\);
Consequently,, Charu completes = \(W - \frac{W}{6} - \frac{4W}{10} = \frac{26W}{10} = \frac{13W}{30}\)
hence, Charu's proportion = \(\frac{13}{30} \times 21000 = 9100\)