CAT 2023 Slot 1 Solved Paper

Let us assume the efficiencies of Amal, Sunil, and Kamal are a, s, and k, respectively.
Given that they are in H.P.
⇒‌

2

s

=‌

1

a

+‌

1

k

−−(1)
Also, given that Kamal takes twice as much time as Amal to do the same amount of job
⇒a=2k
Given that when Amal and Sunil work for 4 days and 9 days, respectively, Kamal needs to work for 16 days to finish the remaining job.
⇒ If W is the total work ⇒4a+9 s+16k=W.
from (1) ‌

2

s

=‌

1

a

+‌

2

a

⇒a=‌

3

2

s and k=‌

3

4

s
⇒4(‌

3s

2

)+9s+16(‌

3s

4

)=W
⇒6s+9s+12s=W
⇒27s=W⇒s=‌

W

27

⇒ Sunil will take 27 days to finish the work when working alone.