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 : y = P’s share of profit : Q’s share of profit

Therefore,

The profit earned after 2 years will be divided between Smith and Kate in the ratio of 3 : 1.

x : y = P’s share of profit : Q’s share of profit

Therefore,

[latex]\frac {Sham’s share of profit}{Ram’s share of profit} = \frac {84000}{28000} = \frac {Sham’s investment}{Ram’s investment}[/latex]

[latex]\frac {2}{3} = \frac {4000}{X}[/latex]

X = Rs. 60,000

Amount invested by Ram = Rs. 60,000

Hint: Ratio of shares of John, Tyson and Mike = Ratio of their investments

Therefore,

100000 : 150000 : 175000 = 4 : 6 : 7

Now, we have to calculate share belonging to each person from all the shares considering the annual profit.

Total shares = 4 + 6 + 7 = 17 shares

John’s Share = [latex]\frac {4}{17} × 46000 = Rs. 10823.53[/latex]

Tyson’s Share = [latex]\frac {6}{17} × 46000 = Rs. 16235.294[/latex]

Mike’s Share = [latex]\frac {7}{17} × 46000 = Rs. 18941.176[/latex]

Harry : John : Smith = 27000 : 72000 : 81000 = 3 : 8 : 9

Total no. of shares = 3 + 8 + 9 = 20 shares

Smith’s share = [latex]\frac {9}{20}[/latex]

Let total profit = Rs. X

[latex]\frac {36000}{x} = \frac {9}{20}[/latex]

[latex]\frac {36000 \times 20}{9} = 80000[/latex]

Total profit = Rs. 80,000

[latex]\frac {George’s share of profit}{Kate’s share of profit} = \frac {Initial investment of George × Time}{Initial investment of Kate × Time}[/latex]

Always try to simplify this type of numerical by arranging them in table format as shown below:

George | Rs. 50.000 for 3 years | Actual investment = initial investment × months = 50000 × 36 = Rs. 1800000 |

Kate | Rs. 70.000 for 2 years 6 months | Actual investment = initial investment × months = 70000 × 30 = Rs. 2100000 |

Actual investment ratio of George and Kate = [latex]\frac {Actual investment of George}{Actual investment of Kate} = \frac {1800000}{2100000} =\frac {6}{7} [/latex]

George’s share of profit = [latex]\frac {6}{13} \times 25000= Rs. 11538.46[/latex]

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