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.

Then Ashok’s share = Rs. [latex]\frac {3z}{4}[/latex]

Raju’s share =[latex] z – \frac {3z}{4}[/latex]

=[latex]\frac {z}{4}[/latex]

Therefore Raju : Ashok = [latex]\frac {z}{4} : \frac {3z}{4}[/latex]

=z:3z

=1:3

Let the total capital be rs.x and

Suppose Ashok’s money was used for x months

Then, [latex]\frac {(\frac {2x}{5}) \times 5 }{ (\frac {3x}{5}) \times y} = \frac {1}{3}[/latex]

[latex]\frac {10x}{3xy} = \frac {1}{3}[/latex]

10 = y

Thus Ashok’s money was used for 10 months.

Aarthi invested Rs.8x for y months

Then, [latex]\frac {15x \times 6 }{8x \times y} = \frac {45}{16}[/latex]

Y = 4 months

Hence Aarthi invested the money for 4 months.

7’s = 2352

1’s = 336

12’s = 4032

84 % of profit = 4032

[latex](\frac {84}{100}) \times [/latex] Total profit = 4032

Total profit = [latex]4032 \times (\frac {100}{84})[/latex] = 4800

Aakash: Murali : sakthi = 153000:126000:174000

=153:126:174

=51:42:58

Aakash share = Rs [latex](\frac {75500 \times 51}{151})[/latex]

= Rs [latex](500 \times 51)[/latex]

= RS 25500

Murali share = Rs [latex](\frac {75500 \times 42}{151})[/latex]

= Rs [latex](500 \times 42)[/latex]

= Rs 21,000

Sakthi share = Rs [latex](\frac {75500 \times 58}{151})[/latex]

= Rs [latex](500 \times 58)[/latex]

= Rs 29,000

Q = Rs.15000/- per 3 years

R= Rs.22500/- per 4years

P:Q:R = (7500 [latex]\times[/latex] 2): (15000 [latex]\times[/latex] 3):(22500 [latex]\times[/latex] 4)

P:Q:R = 15000:45000:90000

P:Q:R =15:45:90

P:Q:R =1:3:6

Then, R’s share is,

=Rs [latex](\frac {6}{10 \times 4200})[/latex]

=Rs 2520

Hence the required answer is Rs 2520

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