Total profit = Rs. 1,60,000
Prakash's share = 41 of profit = 41×1,60,000 = Rs. 40,000
Since Prakash has a guarantee of minimum Rs. 50,000, but his actual share is only Rs. 40,000, he will receive the guaranteed amount of Rs. 50,000.
Deficiency to be borne by old partners = 50,000 - 40,000 = Rs. 10,000
The remaining profit after Prakash's normal share = 1,60,000 - 40,000 = Rs. 1,20,000
This Rs. 1,20,000 is distributed between Vijay and Manohar in their profit-sharing ratio of 2:1:
Vijay's share = 1,20,000×32 = Rs. 80,000
Manohar's share = 1,20,000×31 = Rs. 40,000
The deficiency of Rs. 10,000 is also borne by Vijay and Manohar in their ratio 2:1:
Vijay bears = 10,000×32 = Rs. 6,667
Manohar bears = 10,000×31 = Rs. 3,333
Final profit for Vijay = 80,000 - 6,667 = Rs. 73,333
Verification: Vijay (73,333) + Manohar (36,667) + Prakash (50,000) = Rs. 1,60,000 ✓