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⁞ Partnership

Aptitude ➤ Partnership ➤ 1

1. Partnership: When two or more than two persons run a business jointly, they are called partners and the deal is known as partnership.

2. Ratio of Division of Gains:

i) When investments of all the partners are for the same time, the gain or loss is distributed among the partners in the ratio of their investments. Suppose A and B invest Rs. x and Rs. y respectively for a year in a business, then at the end of the year:

(A’s share of profit) : (B's share of profit) = x : y.

ii) When investments are for different time periods, then equivalent capitals are calculated for a unit of time by taking (capital x number of units of time). Now, gain or loss is divided in the ratio of these capitals. Suppose A invests Rs. x for p months and B invests Rs. y for q months, then

(A’s share of profit) : (B's share of profit) = xp : yq.

3. Working and Sleeping Partners: A partner who manages the business is known as a working partner and the one who simply invests the money is a sleeping partner.

Question 6
Q6.  A starts business with Rs. 3500 and after 5 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2 : 3. What is B's contribution in the capital ?
 

Answer :  Rs. 9000


Let B's capital be Rs. x.
Then, their ratios are , 3500 X 12 : 7x = 2 : 3
⇒ 42000/7x = 2/3
⇒ x = Rs. (42000 X 3) / (2 X 7)
= Rs. (42000 X 3) / 14
= Rs. 3000 X 3
= Rs. 9000.
⚔ DISCUSS

Question 7
Q7.  A and B entered into partnership with capitals in the ratio 4 : 5. After 3 months, A withdrew one-fouth of his capital and B withdrew one-fifth of his capital. The gain at the end of 10 months was Rs. 760. A's share in this profit is:
 

Answer :  Rs. 330


Their capitals be Rs 4x and 5x.
Then their ratios are
A : B = [ (4x X 3) + ( 4x - (1/4)4x )X7 ] : [ (5x X 3) + ( 5x - (1/5)5x )X7 ] .
= 12x + 21x : 15x +28x
= 33x : 43x
= 33 : 43

∴ A's share = 760 X (33/76) = Rs. 330
⚔ DISCUSS

Question 8
Q8.  Four milkmen rented a pasture. A grazed 24 cows for 3 months; B 10 cows for 5 months; C 35 cows for 4 months and D 21 cows for 3 months. If A's share of rent is Rs. 720, find the total rent of the field.
 

Answer :  Rs. 3250


Ratio of shares of A, B, C, D

= (24 x 3) : (10 x 5) : (35 x 4) : (21 x 3)
= 72 : 50 : 140 : 63.

Let total rent be Rs. x. Then,
A's share = Rs. (72x)/325

∴ (72x)/325 = 720 ⇔ x = (720 x 325)/72 = 3250

Hence, total rent of the field is Rs. 3250.
⚔ DISCUSS

Question 9
Q9.  A, B, C rent a pasture. A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing. If the rent of the pasture is Rs. 175, how much must C pay as his share of rent?
 

Answer :  Rs. 45


Ratio of shares of A, B, C

A : B : C = (10 x 7) : (12 x 5) : (15 x 3)
= 70 : 60 : 45
= 14 : 12 : 9.

C's rent = Rs. 175 x (9/35) = Rs. 45.
⚔ DISCUSS

Question 10
Q10.  A and B started a partnership business investing some amount in the ratio of 3 : 5. C joined then after six months with an amount equal to that of B. In what proportion should the profit at the end of one year be distributed among A, B and C?
 

Answer :  6 : 10 : 5


Let the initial investments of A and B be 3x and 5x.

A : B : C = (3x X 12) : (5x X 12) : (5x X 6)
= 36 : 60 : 30
= 6 : 10 : 5
⚔ DISCUSS

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