P, Q, and R are partners in a business. Their investments are in the ratio 1/2 : 1/3 : 1/6 respectively. Q withdraws half of his capital after 6 months. The business runs for 18 months. If the total profit is Tk 10,800, what is R’s share of the profit?

Question: P, Q, and R are partners in a business. Their investments are in the ratio 1/2 : 1/3 : 1/6 respectively. Q withdraws half of his capital after 6 months. The business runs for 18 months. If the total profit is Tk 10,800, what is R’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.

P : Q : R = (3x × 18) : (2x × 6) + (2x × 1/2 × 12) : (x × 18) [Q's portion was calculated as half after the first 6 months.]
= 54x : 24x : 18x
= 9 : 4 : 3

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

Total profit = Tk 10,800

∴ R’s share = 10800 × (3/16)
= 2025

∴ R’s share of the profit is Tk 2025.