cat 2021 Question 6

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

Accepted Answer

Let entire work be $W$.

Now Anil worked for $24$ days.

Bimal worked for $14$ days and Charu worked for $14$ days.

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:

$\frac{13}{30} imes 21000 = 9100$.

Question 6.

Question Explanation