# Partnership

• Concepts:

Simple Partnership:

Here capitals of partners are invested for same period and profit or loss is divided in the ratio of their investments.

(Investment of A/Investment of B ) = (Profit of A/Profit of B ) or (Loss of A/Loss of B )

(Investment of A: Investment of B: Investment of C) = (Profit of A: Profit of B: Profit of C) or (Loss of A: Loss of B: Loss of C)

Compound Partnership

Here capitals are invested for different periods and profit or loss is divided in the ratio of their monthly equivalent investment.

Monthly equivalent is the product of the capital invested and period for which it is invested.

(Monthly Equivalent investment of A/ Monthly Equivalent Investment of B ) = (Investment of A * Period of Investment of A) / (Investment of B * Period of Investment of B ) = (Profit of A)/(Profit of B ) or (Loss of A)/(Loss of B )

If three partners are there profit or loss is divided in the ratio of their monthly equivalent investment.

Questions

A and B start a business. A invests Rs.600 more than B for 4 months and B for 5 months. A’s share is Rs.48 more than that of B out of a total profit of Rs.528. Find the capital contributed by each?

A’s profit + B’s profit = 528
B’s profit +B’s profit+48 = 528
2 * B’s profit = 480
B’s profit = 240; A’s profit = 288
A’s capital * 4/B’s capital * 5 = 288/240 = 6/5
A’s capital/B’s capital = 6/4 = 3/2
B’s capital + 600/B’s capital = 3/2
2 * B’s capital +1200 = 3* B’s capital
B’s capital = Rs.1200; A’s capital = Rs.1800

Two partners invested Rs.1250 and Rs.850 respectively in a business. They decided to distribute equally 60% of the profit and the remaining as the interest on their capital. If one receives Rs.320 more than the other, find the total profit.

Let x is total profit.
Both partners will get 0.3x each.
Remaining 0.4x will be divided in the ratio of 1250/850 => 25/17
One will get 0.3x+ (10x/42) and other will get 0.3x+(6,8x/42)
22.6x/42 – 19.4x/42 = 320
3.2x = 42 *320
X = 4200
Hence total profit is Rs.4200.

A and B enter in to a partnership. A puts in Rs.2000 but at the end of three months, withdraws Rs.500 and again at the end of 8 months withdraws Rs.300. Out of a total profit of Rs.900 at the end of the year, B’s share was Rs.400. Find B’s capital.

A’s profit/B’s profit = 5/4
A’s capital = 2000*3 + 1500 * 5 +1200 *4 = 6000+7500+4800 = 18300
A’s capital/ B’s capital = 5/4
B’s capital for 12 months= 4 * 18300/5 = 4 * 3660 = 14640
B’s capital for one month = 14640/12 = Rs.1220

A, B and C started a business, two times of A’s capital is equal to 3 times of B’s capital and equal to 5 times of C’s capital. Out of a profit of Rs.1550, A’s share is

2A = 3B = 5C
A : B = 3:2
B:C = 5:3
A:B:C = 15:10:6
A’s share = 1550 * 15/(15+10+6) = 50 * 15 = Rs.750

Raju, Ravi and Ramu invest Rs.15000, Rs.25000 and Rs.30000 respectively in a business. After one year Raju removed his money but Ravi and Raju continued for one more year. If the net profit after 2 years is Rs.25200, then Raju’s share in the profit is:

Raju’s capital = 1 * 15000 = 15000
Ravi’s capital = 2 * 25000 = 50000
Ramu’s capital = 2 * 30000 = 60000
Raju’s share = 25200 * 15000/125000 = 25200 * 3/25 = 1008 * 3 = Rs.3024

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