X, Y, and Z are partners in a business. Their investments are in the ratio 1/2 : 1/3 : 1/6 respectively. Y withdraws half of his capital after 4 months. The business runs for 12 months. If the total profit is Tk 9,600, what is Z's share of the profit?

Question: X, Y, and Z are partners in a business. Their investments are in the ratio 1/2 : 1/3 : 1/6 respectively. Y withdraws half of his capital after 4 months. The business runs for 12 months. If the total profit is Tk 9,600, what is Z's share of the profit?

Solution:
Ratio of initial investments = 1/2 : 1/3 : 1/6
= 3 : 2 : 1

Let their initial investments be 3x, 2x, and x respectively.

X : Y : Z = (3x × 12) : (2x × 4) + (2x × 1/2 × 8) : (x × 12)
= 36x : (8x + 8x) : 12x
= 36x : 16x : 12x
= 9 : 4 : 3

Sum of the ratio = 9 + 4 + 3 = 16

Total profit = Tk 9,600
∴ Z's share = 9600 × (3/16)
= 28800/16
= 1800
∴ Z's share of the profit is Tk 1,800