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.

X = 9000

Investment made by A, B , C – 36000, 45000, 54000

Ratio in which the profit will divide- [latex]36000 \times 12 : 45000 \times 2 : 54000 \times 6 + 27000 \times 6 [/latex]

i.e 4:5:9. So C share = [latex](\frac {9}{18}) \times 60000[/latex] = 30000

[latex](\frac {6 \times {t}_{1}}{7 \times {t}_{1}}) = \frac {3}{1}[/latex], u will get [latex](\frac {{t}_{1}}{{t}_{2}}) = 5:2[/latex]

Similarly, [latex]( \frac {5 \times{t}_{2}}{7 \times {t}_{3}}) = \frac {1}{5}[/latex] u will get [latex]\frac {{t}^{2}}{{t}^{3}} = \frac {7}{25}[/latex]

So, to find X – [latex]\frac {(4x + 4300)}{(5x - 3200)} = \frac{5}{4}[/latex]

So investment made by A = [latex](\frac {33200}{9}) \times 4 = 14755.55 [/latex]

So total amount invested by A and C = [latex](\frac {8}{12}) \times 24000 = 16000[/latex]

[latex]12P : 3000 \times 6[/latex]

P : 1500

So Rahul share = [latex][\frac{p}{(1500 + p)}] \times 9000 = 5000[/latex]

[latex]P = 75 \times 25 = 1875[/latex]

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