CAT 2021 Slot 2 QA Question & Solution

ArithmeticEasy

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

Options

9000

9200

9100

9150

Solution

Let Entire work be W
Now Anil worked for 24 days
Bimal worked for 14 days and Charu worked for 14 days .
Now Anil Completes W in 60 days
so in 24 days he completed 0.4W
Bimal completes W in 84 Days
So in 14 Days Bimal completes = $\frac{W}{6}$
Therefore work done by charu = $W-\frac{W}{6}-\frac{4W}{10}$= $\frac{26W}{10}$=$\frac{13W}{30}$
Therefore proportion of Charu = $\frac{13}{30}\times\ 21000$=9100