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.

= 21000:17500 = 210:175 = 42:35 = 6:5

Share of X in the profit

= [latex] 26400 \times \frac {6}{11} = 2400 \times 6 = 14400[/latex]

= Ratio of the investments multiplied by the time period

= [latex] 45000 \times 12:30000 \times 9[/latex]

= [latex] 45 \times 12:30 \times 9[/latex]

= [latex] 3 \times 12:2 \times 9[/latex]

= 2:1

Assume that investment of C = x

Then investment of B = 5000 + x

Investment of A = 4000 + 5000 + x = 9000 + x

x + 5000 + x + 9000 + x = 50000

⇒ 3x + 14000 = 50000

⇒3x = 50000 – 14000 = 36000

⇒ x = [latex]\frac {36000}{3} = 12000[/latex]

Investment of C = x = 12000

Investment of B =5000 + x = 17000

Investment of A = 9000 + x = 21000

Ratio of the investment of A, B and C

= 21000:17000:12000

= 21:17:12

Share of A = Total profit [latex]\times \frac { 21}{50}[/latex]

= [latex] 35000 \times \frac { 21}{50}= 700 \times 21=14700[/latex]

40000: q = 2:3

⇒ 40000 × 3 = 2q

⇒ q = [latex]\frac {40000 \times 3}{2}[/latex] = 60000

Here A's and B's capitals are there for equal time.

Hence

A: B = 85000:15000

= 85: 15

= 17: 3

Hence

A: B = 85000:15000

= 85: 15

= 17: 3

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