Explanation:

Tony, Monu and James completed a work together in 36 days.
In one day, together they will finish 1/36 of work.
Out of Rs. 54000, Tony took half of the total money,
Monu took one third and James took remaining.
The shares of Tony, Monu and James are in ratio
1/2 : 1/3 : (1 - 1/2 - 1/3) i.e.,  3 : 2 : 1
We know that efficiencies are in the same ratio as the share received in total amount.
Let us suppose that work done by Tony, Monu and James in one day is 3T, 2T and T, respectively,
⇒ 3T + 2T + T = 1/36
⇒ 6T = 1/36
⇒ T = 1/216
Work done by Tony in one day = 3T = 3/216 = 1/72
Work done by James in one day = T = 1/216
Let us suppose that when Tony and James work together, they take N days to finish the work.
⇒ N/72 + N/216 = 1
⇒ 4N/216 = 1
⇒ N = 54
∴  When Tony and James work together, they take 54 days to finish the work.