# 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:

Karan started a business investing Rs 29000. After five months, Satish joined with a capital of Rs 18000. If at the end of the year, they earn a profit of Rs. 16970, then what will be the share of Satish in the profit ?

 A) Rs. 5422 B) Rs. 5489 C) Rs. 4511 D) Rs. 6145

Explanation:

Now as per question, Karan invested for 12 months and Satish invested for 7 months.

So, Karan:Satish = (29000 x 12):(18000 x 7)

= 348:126

= 58:21

Satish Ratio in profit will be= $16970×2179$ = Rs. 4511

7 8767
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

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

8125
Q:

Three friends had dinner at a restaurant. When the bill was received, Akshitha paid 2/3 as much as Veena paid and Veena paid 1/2 as much as Lasya paid. What fraction of the bill did Veena pay ?

 A) 11/3 B) 2/13 C) 3/11 D) 13/4

Explanation:

Let Veena paid x,
so Akshitha paid 2x/3 , and Lasya paid 2x,
So total bill paid is given by
x+(2x/3) +2x = 1, we get
i.e. x = 3/11

10 7915
Q:

A and B entered into a partnership investing Rs. 13,000 and Rs. 12,000 respectively.After 3 months, A withdrew Rs. 5000 while B invested Rs. 5000 more, After 3 more months, C  joins the business with a capital of Rs. 21,000, The share of B exceeds that of C, out of a total profit of Rs. 26,400 after one year by

 A) 3500 B) 3600 C) 3700 D) 3800

Explanation:

A : B : C = (16000 * 3 + 11000 * 9) : (12000 * 3 + 17000 * 9) : (21000 * 6)

= 147 : 189 : 126

= 7 : 9 ; 6.

Difference of B and C's shares = Rs.  ( 26400 * 9/22 - 26400 * 6/22 ) = Rs. 3600.

10 7823
Q:

Three milkmen rented a pasture. A grazed 24 cows for 4 months; B 10 cows for 6 months; C 56 cows for 5 months. If A's share of rent is Rs. 960, find the total rent of the field?

 A) 4530 B) 4440 C) 4360 D) 4280

Explanation:

Ratio of shares of A,B,C = (24 x 4) : (10 x 6) : (56 x 5)

= 96 : 60 : 280.

Let total rent be Rs. x. Then, A's share = $Rs.96x436$

Hence total rent of the field is Rs. 4360.

8 7482
Q:

Madhu started a business and he invested in 76000, After some month, Amar came to join with him and invest 57000.The end of the year the total profit was divided among them into ratio form 2 : 1.Find after how many months Amar join.

 A) 7 months B) 8 months C) 3 months D) 4 months

Explanation:

we can assume that Amar join into business after x months. So Amar money was invest into  (12 – x ) months.

$76000×1257000×(12-x)=21$

--> 912000 = 114000 ( 12 – x ) = 114 ( 12 – x ) = 912

--> x = 4

After 4 months amar join the business.

3 7479
Q:

Rs. 700 is divided among A, B, C so that A receives half as much as B and B half as much as C. Then C's share is

 A) Rs 200 B) Rs 300 C) Rs 400 D) Rs 500

Explanation:

Let C = x.
Then B = x/2
and A = x/4

A:B:C = 1:2:4.
C's share Rs.[(4/7)*700) = 400

10 7442
Q:

Ram and Raj start a business with investments of Rs. 2500 and Rs. 2250 respectively. After 2 months, Ram takes out Rs.1250 from his capital. After 1 more month, Raj takes out Rs.750 of his capital while Rakesh joins them with a capital of Rs. 3500. At the end of 6 months, they earn a profit of Rs. 2540. Which of the following is the share of each member in the profit ?

 A) Ram - Rs. 800, Raj - Rs. 900, Rakesh - Rs. 840 B) Ram - Rs. 900, Raj - Rs. 800, Rakesh - Rs. 840 C) Ram - Rs. 840, Raj - Rs. 920, Rakesh - Rs. 840 D) Ram - Rs. 800, Raj - Rs. 900, Rakesh - Rs. 940

Answer & Explanation Answer: A) Ram - Rs. 800, Raj - Rs. 900, Rakesh - Rs. 840

Explanation:

Initial investment of Ram = Rs.2500.
After 2 months he withdraw Rs.1250 from his capital.
Therefore, we have, Ram invested Rs.2500 for 2 months and Rs.(2500-1250=) 1250 for 4 months.

Raj invested Rs. 2250 for 3 months and Rs.(2250-750=) 1500 for 3 months.

And, Rakesh invested Rs.3500 for 3 months;

Their investing ratio:
Ram:Raj:Rakesh = (2500x2 + 1250x4):(2250x3 + 1500x3):(3500x3)
= (10,000):(11,250):(10,500) = 1000:1125:1050 = 40:45:42

Total profit for 6 months = Rs.2540
Therefore, Ram's share = Rs.(2540 x 40/(40+45+42)) = Rs.(2540 x 40/127) = Rs.800
Raj's share = Rs.(2540 x 45/127) = Rs.900
Rakesh's share = Rs.(2540 x 42/127) = Rs.840