Prabodh has done 1/2 of a job in 30 days, Sapan completes the rest of the job in 45 days. In how many days can they together do the job?

1. Find Prabodh's rate of work:
Prabodh does
2
1
​
of the job in 30 days.
Therefore, time taken by Prabodh to complete the full job (P) is:

P=30×2=60 days
Prabodh's 1-day work rate =
60
1
​


Find Sapan's rate of work:
The remaining work is 1−
2
1
​
=
2
1
​
of the job. Sapan completes this rest of the job in 45 days.
Therefore, time taken by Sapan to complete the full job (S) is:

S=45×2=90 days
Sapan's 1-day work rate =
90
1
​


Combined work rate:
Combined 1-day work rate of Prabodh and Sapan together:

Rate=
60
1
​
+
90
1
​
=
180
3+2
​
=
180
5
​
=
36
1
​

Since their combined work rate is
36
1
​
per day, they can complete the entire job together in 36 days.