1. Suppose A and B invest Rs. [latex]x[/latex] and Rs. [latex]y[/latex] respectively for a year in a business, then at the end of the year:

(A's share of profit) : (B's share of profit) = [latex]x[/latex] : [latex]y[/latex]

Here investment of all partners are for same time, and the gain or loss is distributed among them in the ratios of their investments.

2. Suppose A invests Rs. [latex]x[/latex] for 'p' months and B invests Rs. [latex]y[/latex] for 'q' months, then

(A's share of profit) : (B's share of profit) = [latex]x[/latex]p : [latex]x[/latex]q

Here investments are for different time periods, equivalent capitals are calculated for a unit of time by taking,

(capital x number of units of time).

Profit or loss is divided in the ratio of these capitals.

Here first person invested amount A for [latex]t_{1} [/latex] period, second persons invested amount B for [latex]t_{2} [/latex] period and so on.

L = K + [latex]\frac {M}{4}[/latex]

2 : 1 : 3 = [latex]\frac {9750 \times 3}{6} = 4875[/latex]

Sahir = [latex]\frac {22500 \times 4}{9} = 10000[/latex]

[latex]\frac {1}{2}[/latex] : 1 [latex]\Rightarrow[/latex] 1 : 2

Ratio of Profit = 4 : 2 = 2 : 1

Ratio of Profit = 4 : 2 = 2 : 1

B gets 25% of 30,000 = 7,500

Profit left which is to be divided in ratio 2 : 3 = 30,000 - 7,500 = 22,500

Now N gets [latex]\frac {3}{(2 + 3)} \times 22,500 = 13,500[/latex]

So total share B = 7500 + 13500 = Rs 21,000

So B : A : C = [latex]1 \times 3 : 4 \times 3 : 4 \times 2 = 3 : 12 : 8[/latex]

Share of A = [latex][\frac {12}{(3 + 12 + 8)}] \times 35,650[/latex] = Rs 18,600

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