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.

80 : 72 : 15x

So [latex]\frac {80}{(80 + 72 + 15x} \times 5675 = 2000[/latex]

Solve, x = 5

Remaining = [latex]\frac {4X}{5} = B + C[/latex]

B = [latex]\frac {X}{2} [/latex], C = [latex]\frac {4X}{5} - \frac {x}{2} = \frac {3x}{10} [/latex]

[latex]\frac {x}{5} : \frac {x}{2} : \frac {3x}{10} = 2 : 5 : 3[/latex]

[latex]\frac {7200 \times 5}{10} = 3600[/latex]

[latex]38500 \times 12 : 49500 \times 12 : x \times 12 = 7 : 9 : 12x = 7 : 9 : 13[/latex]

Profit = [latex] \frac {101500 \times 13}{29} = 45500[/latex]

19,20,000 = 80x

x = [latex]\frac {1920000}{80} = 24,000[/latex]

Remaining = Rs.6,08,000

x = [latex]\frac {608000 \times 3}{12} = 1,52000[/latex]

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