Unit 4 Exercise 4.2 Q.NO.4(ii,iii,iv,v), Sindh Text Book Board Jamshoro

Unit 4 Exercise 4.2 Q.NO.4 Sindh Text Book Board Jamshoro

Partnership math involves calculating how to divide profits or losses among partners based on their investments and the duration of those investments. The basic principle is that a partner's share of the profit is proportional to the product of their investment and the time they invested. The formula for this is often expressed as a ratio of the product of capital (



Ccap C

𝐶

) and time (



Tcap T

𝑇

) for each partner, such as



P1∶P2=C1×T1∶C2×T2cap P sub 1 colon cap P sub 2 equals cap C sub 1 cross cap T sub 1 colon cap C sub 2 cross cap T sub 2

𝑃1∶𝑃2=𝐶1×𝑇1∶𝐶2×𝑇2

. 

Simple partnership 

Scenario: All partners invest for the same amount of time.

Formula: The profit is divided in the same ratio as the investments.

Example: If Partner A invests



Xcap X

𝑋

and Partner B invests



Ycap Y

𝑌

for the same time, the profit ratio is



X∶Ycap X colon cap Y

𝑋∶𝑌

. 

Compound partnership 

Scenario: Partners invest different amounts for different durations.

Formula: The profit is divided in the ratio of the product of each partner's investment and time.

Formula:



P1∶P2=(C1×T1)∶(C2×T2)cap P sub 1 colon cap P sub 2 equals open paren cap C sub 1 cross cap T sub 1 close paren colon open paren cap C sub 2 cross cap T sub 2 close paren

𝑃1∶𝑃2=(𝐶1×𝑇1)∶(𝐶2×𝑇2)

Example: If Partner A invests



C1cap C sub 1

𝐶1

for time



T1cap T sub 1

𝑇1

and Partner B invests



C2cap C sub 2

𝐶2

for time



T2cap T sub 2

𝑇2

, the profit ratio is



(C1×T1)∶(C2×T2)open paren cap C sub 1 cross cap T sub 1 close paren colon open paren cap C sub 2 cross cap T sub 2 close paren

(𝐶1×𝑇1)∶(𝐶2×𝑇2)

.

To find an individual share: Calculate the ratio of the products for each partner, then divide the total profit by the sum of the ratio parts, and multiply that value by the individual partner's part of the ratio.

Example: With a profit of



$550$ 550

$550

, Jim invested



$2000$ 2000

$2000

for 12 months, and Nancy invested



$2500$ 2500

$2500

for 8 months.

Jim's profit ratio:



2000×12=240002000 cross 12 equals 24000

2000×12=24000

Nancy's profit ratio:



2500×8=200002500 cross 8 equals 20000

2500×8=20000

Ratio of profit:



24000∶2000024000 colon 20000

24000∶20000

, which simplifies to



6∶56 colon 5

6∶5

.

Jim's share:



(66+5)×550=300open paren the fraction with numerator 6 and denominator 6 plus 5 end-fraction close paren cross 550 equals 300

(66+5)×550=300

.

Nancy's share:



(56+5)×550=250open paren the fraction with numerator 5 and denominator 6 plus 5 end-fraction close paren cross 550 equals 250

(56+5)×550=250

.