# Partnership Questions

FACTS  AND  FORMULAE  FOR  PARTNERSHIP  PROBLEMS

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

Ratio of Division of Gains:

(i) When investments of all the partners are for the same time, the gain or loss is distributed a 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.

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.

Q:

Rs.1200 divided among P, Q and R. P gets half of the total amount received by Q and R. Q gets one-third of the total amount received by P and R. Find the amount received by R ?

 A) Rs. 1100 B) Rs. 500 C) Rs. 1200 D) Rs. 700

Explanation:

Let the amounts to be received by P, Q and R be p, q and r.
p + q + r = 1200
p = 1/2 (q + r) => 2p = q + r

Adding 'p' both sides, 3p = p + q + r = 1200
=> p = Rs.400

q = 1/3 (p + r) => 3q = p + r

Adding 'q' both sides, 4q = p + q + r = 1200
=> q = Rs.300

r = 1200 - (p + q) => r = Rs.500.

16 21195
Q:

Anand and Deepak started a business investing Rs. 22,500 and Rs. 35,000 respectively. Out of a total profit of Rs. 13,800, Deepak's share is :

 A) 8400 B) 8200 C) 8100 D) 8000

Explanation:

Ratio of their shares = 22500 : 35000 = 9 : 14.

Deepak's share = Rs. (13800 * 14/23) = Rs. 8400.

35 20267
Q:

The ratio of investments of two partners is 11:12 and the ratio of their profits is 2 : 3. If A invested the money for 8 months , find for how much time B invested his money.

Suppose A invested Rs.11 for 8 months and B invested Rs. 12 for x months.

$\inline&space;\therefore$ Ratio of investments of A and B

= (11 x 8) : (12 x x)

= 88 : 12x

$\inline&space;\therefore$ $\inline&space;\frac{88}{12x}=\frac{2}{3}\Rightarrow&space;x=11$

20116
Q:

P and Q started a business investing Rs, 85,000 and Rs. 15,000 respectively. In what ratio the profit named after 2 years bo divided between P and Q respectively ?

 A) 17:23 B) 17:3 C) 17:33 D) 3:4

Explanation:

P : Q = 85000 : 15000 = 86 : 15 = 17 : 3 .

20 19971
Q:

A,B and C enter into a partnership in the ratio  $72:43:65$. After 4 months, A increases his share by 50%. If the total profit at the end of one year be Rs. 21600, then B's share in the profit is :

 A) Rs. 4000 B) Rs. 6000 C) Rs. 9000 D) Rs. 3000

Explanation:

Given ratio of initial investments = $72:43:65$ = 105 : 40 : 36.

Let the initial investments be 105x, 40x and 36x.

= 1680x : 480x : 432x = 35 : 10 : 9.

Hence, B's share = $21600×1054$ = Rs. 4000.

17 19001
Q:

Three friends, P, Q and R started a partnership business investing money in the ratio of 5 : 4 : 2 respectively for a period of 3 years. What is the amount received by P as his share in the total profit ?

a. Total amount invested in the business in Rs. 22,000.

b. Profit earned at the end of 3 years is 3/8 of the total investment.

c. The average amount of profit earned per year is Rs. 2750.

 A) Only c is sufficient B) Both a & b are sufficient C) Both A & B gives result D) None

Explanation:

a and b give, profit after 3 years = Rs.(3/8 x 22000) = Rs.8250.

From c also, profit after 3 years = Rs. (2750 x 3) = Rs. 8250.

∴ P's share = Rs.(8250 x 5/11) = Rs. 3750.

Thus, (either C is redundant) or (a and b are redundant).

5 18613
Q:

Three partners shared the profit in a business in the ratio 4:6:8. They had partnered for 12 months, 8 months and 6 months respectively. What was the ratio of their investments?

 A) 4:6:8 B) 4:7:8 C) 4:8:16 D) 4:9:16

Explanation:

Let their investments be Rs. x for 12 months, Rs. y for 8 months and Rs. z for 6 months respectively.

Then, 12x : 8y : 6z = 4 : 6 : 8

Now, 12x/8y = 4/6   <=>   9x=4y   <=>   y=9x/4

And, 12x/6z = 4/8   <=>   4x=z     <=>    z=4x

Therefore, x : y: z  =  x : 9x/4: 4x  =  4 : 9 : 16

21 18486
Q:

In a business, A and C invested amounts in the ratio 2:1, whereas the ratio between amounts invested by A and B was 3:2. If Rs. 1,57,300 was their profit, how much amount did B receive ?

 A) 48400 B) 54200 C) 64000 D) 74000