Pannalal has done
3
1
​
rd of a job in 20 days, Saiprasad completes the rest of the job in 10 days. In how many days can they together do the job?

Pannalal completes
3
1
​
of the job in 20 days.

Therefore, the total time required by Pannalal to complete the whole job alone (T
P
​
) is:

T
P
​
=20×3=60 days
The remaining work is:

1−
3
1
​
=
3
2
​

Saiprasad completes this remaining
3
2
​
of the job in 10 days.

Therefore, the total time required by Saiprasad to complete the whole job alone (T
S
​
) is:

T
S
​
=10×
2
3
​
=15 days
Let's find the time taken when they work together (T
total
​
):

T
total
​

1
​
=
T
P
​

1
​
+
T
S
​

1
​

T
total
​

1
​
=
60
1
​
+
15
1
​

Taking the LCM of 60 and 15, which is 60:

T
total
​

1
​
=
60
1+4
​
=
60
5
​
=
12
1
​

T
total
​
=12 days