The correct answer is option (C):
5,85,000
Let's break down this profit-sharing problem step-by-step. The key to solving this is understanding how the capital contributed affects the profit share and how the time each person invested in the business impacts their share.
First, identify the pattern in the capital contributions. The contributions decrease by 2,000 each month, starting from A (24,000) down to L (2,000). Also, note that the partners joined one by one, each one month after the previous one. A invested for the whole year.
We are given that D got 72,000 more than L. Since the profit is shared based on capital and time, we can use this information to create an equation.
Let's represent the profit shares of each partner with variables:
* A's profit share: Pa
* B's profit share: Pb
* C's profit share: Pc
* D's profit share: Pd
* L's profit share: Pl
Capital contributed by each person is:
* A = 24,000
* B = 22,000
* C = 20,000
* D = 18,000 (Because the capital contribution decreases by 2000 per month)
* E = 16,000
* F = 14,000
* G = 12,000
* H = 10,000
* I = 8,000
* J = 6,000
* K = 4,000
* L = 2,000
Time investment in months is:
* A invested for 12 months
* B invested for 11 months
* C invested for 10 months
* D invested for 9 months
* E invested for 8 months
* F invested for 7 months
* G invested for 6 months
* H invested for 5 months
* I invested for 4 months
* J invested for 3 months
* K invested for 2 months
* L invested for 1 month
Profit share is proportional to (Capital * Time).
Let the total profit be P. We can set up the ratio of profit shares relative to the total profit:
Pa = (24000 * 12)/ X * P
Pb = (22000 * 11)/ X * P
Pc = (20000 * 10)/ X * P
Pd = (18000 * 9)/ X * P
Pe = (16000 * 8)/ X * P
Pf = (14000 * 7)/ X * P
Pg = (12000 * 6)/ X * P
Ph = (10000 * 5)/ X * P
Pi = (8000 * 4)/ X * P
Pj = (6000 * 3)/ X * P
Pk = (4000 * 2)/ X * P
Pl = (2000 * 1)/ X * P
Where X is the sum of (Capital * Time) for all partners.
X = (24000 * 12) + (22000 * 11) + (20000 * 10) + (18000 * 9) + (16000 * 8) + (14000 * 7) + (12000 * 6) + (10000 * 5) + (8000 * 4) + (6000 * 3) + (4000 * 2) + (2000 * 1)
X = 288000 + 242000 + 200000 + 162000 + 128000 + 98000 + 72000 + 50000 + 32000 + 18000 + 8000 + 2000 = 1300000
We are given Pd - Pl = 72,000. Substituting the values we have above:
(18000 * 9) / 1300000 * P - (2000 * 1) / 1300000 * P = 72,000
162000/1300000 * P - 2000/1300000 * P = 72000
160000/1300000 * P = 72000
P = 72000 * (1300000 / 160000)
P = 72000 * (130/16)
P = 72000 * 8.125
P = 585000
Therefore, the total profit is 585,000.