Partnership

1.A, B and C invested capitals in the ratio 3 : 4 : 9; the timing of their investments being in the ratio 9 : 6 : 7. In what ratio would their profit be distributed? 

(a) 9 : 8 : 21

(b) 27 : 25 : 63

(c) 27 : 24 : 36

(d) 9 : 8 : 12 

1.(a)

2.A, B and C invest their capitals in a business. If the ratio of their periods of investments are 7 : 3 : 5 and their profits are in the ratio of 2 : 1 : 2. Find the ratio in which the investments are made by A, B and C. 

(a) 30 : 35 : 42

(b) 7 : 6 : 10 

(c) 42 : 30 : 35 

(d) 42 : 25 : 35 

2.(a)

3.A, B and C are partners. A receives 2/5 of the profit and B and C share the remaining profit equally. A’s income is increased by Rs. 220 when the profit rises from 8% to 10%. Find the capitals invested by A, B and C.

(a)8850

(b)8860

(c)8250

(d)8230

3.(c)        Soln: 

Detail Method: For A’s share: (10% – 8%) = Rs. 220

∴ 100% ≡220/2×100= Rs. 11000

∴ A’s capital ≡Rs. 11000

For B’s & share: 2/5≡ 11000

∴3/5≡11000/2×3≡ Rs. 16500

∴ B’s and C’s capitals are Rs. 8250 each. 

Quicker Method: Applying the above rule, we have, 

A’s capital = (100×220)/(10-8)= Rs. 11000 

B’s and C’s capitals = ((100 × 220)/(10 - 8)  × (1- 2/5))/2

= Rs. 8250 each. 

4.A, B and C are partners. A receives 2/7 of the profit and B and C share the remaining profit equally. A’s income is increased by Rs. 240 when the profit rises from 10% to 15%. Find the capitals invested by B and C. 

(a) Rs. 2400

(b) Rs. 1200

(c) Rs. 4800

(d) Rs. 6000

4.(d)

5.Two partners invest Rs. 125,000 and Rs. 85,000 respectively in a business and agree that 60% of the profit should be divided equally between them and the remaining profit is to be treated as interest on capital. If one partner gets Rs. 300 more than the other, find the total profit made in the business. 

(a)3937.50

(b)3936.50

(c)3936.55

(d)3937.56

5.(a)

Soln: Detail Method: The difference counts only due to the 40% of the profit which was distributed according to their investments. 

Let the total profit be Rs x. 

Then 40% of x is distributed in the ratio 125,000 : 85,000 = 25 : 17 

Therefore, the share of the first partner 

=40% of x (25/(25+17))

=40% of x (25/42)=40x/100 (25/42)=5x/21

andthe share of the second partner 

=40% of x (17/42)=17x/105

Now, from the question, 

thedifference in share = 5x/21-17x/105=300

or,(x(25-17))/105=300

∴ x = (300×105)/8=Rs.3937.50

Quiker Mothod: Applying the above rule, we have, 

Step I: The ratio of profit = 125,000 : 85,000 = 25 : 17

Step II: total profit = 300(100/40)((25+17)/(25-17))

= Rs. 3937.50 

6.Two partners invest Rs. 24750 and Rs. 16500 respectively in a business and agree that 20% of the profit should be divided equally between them and the remaining profit is to be treated as interest on capital. If one partner gets Rs. 400 more than the other, find the total profit made in the business. 

(a) Rs. 5000

(b) Rs. 2500

(c) Rs. 3500

(d) Rs. 4500

6.(b)

7.A and B invested in the ratio 3 : 2 in a business. If 5% of the total profit goes to charity and A’s share is Rs. 855, find the total profit. 

(a) 1600

(b) 1500

(c) 1400

(d) 1300

7.(b)

8.A and B invested in the ratio 5 : 3 in a business. If 10% of the total profit goes to charity and A’s share is Rs. 900, find the total profit. 

(a) Rs. 1600

(b) Rs. 1400

(c) Rs. 1500

(d) Rs. 1800

8.(a)

Details Method: Suppose the total profit is Rs. 100. 

Then Rs. 5 goes to charity. 

Now, Rs. 95 is divided in the ratio 3 : 2. 

A’s share = 95/(3+2)×3=Rs.57 

But we see that A’s actual share is Rs. 855. 

Actual total profit = 855 (100/57) = Rs. 1500

Quicker Method: Applying the above rule, we have the total profit = 855 (100/(100-5))((3+2)/3)

= 855 (100/95)(5/3)=Rs.1500.

9.Three partners altogether invested Rs. 114,000 in a business. At the end of the year, one got Rs. 337.50, the second Rs. 1125.00 and the third Rs. 675 as profit. How much amount did each invest? What is the percentage of profit? 

(a)1.857%

(b)1.856%

(c)1.866%

(d)1.877%

9.(a)

10.Three partners A, B and C together invested Rs. 375000 in a business. At the end of the year, A got Rs. 52000, B got Rs. 65000 and C got Rs. 78000 as profit. How much amount did A invest? 

(a) Rs. 100000

(b) Rs. 125000

(c) Rs. 150000

(d) Rs. 160000

10.(a)

Soln: 

The ratio of investment = Ratio of profits 

= 337.50 : 1125 : 675

= 3375 : 11250 : 6750 

Dividing each by 1125, we have the ratio = 3 : 10 : 6. 

Shares of the partners = Rs. 114000/(3+10+6)×3,

Rs. 114000/(3+10+6)×10 and Rs.114000/(3+10+6)×6

or, Rs. 18000, Rs. 60000 and Rs. 36000

The required percentage of profit 

=(337.5+1125+675)/114000×100=2137.50/1140=1.857%

Partnership

    Percentage wise distribution of Topics For Tier-II                                          

Partnership

Partnership

What is Partnership?

Partnership: Persons  two or more than two persons when start and run the new  a business  jointly of there own choice, the persons start they are called partners and the deal is done between the partners is known as partnership.

Ratio of Divisions of Gains:
1. 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.

2.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.

1. Three partners shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 8 months and 7 months respectively. What was the ratio of their investments?

A. 5 : 7 : 8

B. 20 : 49 : 64

C. 38 : 28 : 21

D. None of these

2.  P , Q, R enter into a partnership & their share are in the ratio 1/2 : 1/3 : 1/4 , after two months , P withdraws half of the capitals & after 10 months , a profit of Rs 378 is divided among them . What is Q's share?

A. 114

B. 120

C. 134

D. 144

3. A, B, C subscribe Rs. 50,000 for a business. A subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 35,000, A receives:

A. Rs. 8400

B. Rs. 11,900

C. Rs. 13,600

D. Rs. 14,700

4. 29. P, Q, R enter into a partnership. P initially invests 25 lakh & adds another 10 lakhs after one year. Q initially invests 35 lakh & withdrawal 10 lakh after 2 years and R invests Rs 30 Lakhs . In what ratio should the profit be divided at the end of 3 years?

A. 18:19:19

B. 18:18:19

C. 19:19:18

D. 18:19:19

5. A and B started a business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, C joined them with Rs. 20,000. What will be B's share in total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business?

A. Rs. 7500

B. Rs. 9000

C. Rs. 9500

D. Rs. 10,000

6. 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 157300 was their profit, how much amount did B receive?

A. 48000

B. 48200

C. 48400

D. 48600

6. 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?

A. Rs. 45

B. Rs. 50

C. Rs. 55

D. Rs. 60

7. If 4 (P's Capital ) = 6 ( Q's Capital ) = 10 ( R's Capital ) , then out of the total profit of Rs 4650 , R will receive

A. 600

B. 700

C. 800

D. 900

8. Three partners A , B , C start a business . B's Capital is four times C's capital and twice A's capital is equal to thrice B's capital . If the total profit is Rs 16500 at the end of a year ,Find out B's share in it.

A. 4000

B. 5000

C. 6000

D. 7000

9. P and Q invested in a business. The profit earned was divided in the ratio 2 : 3. If P invested Rs 40000, the amount invested by Q is

A. 40000

B. 50000

C. 60000

D. 70000

10. Kamal started a business investing Rs 9000. After five months, Sameer joined with a capital of Rs 8000. If at the end of the year, they earn a profit of Rs. 6970, then what will be the share of Sameer in the profit ?

A. Rs 2380

B. Rs 2300

C. Rs 2280

D. Rs 2260

ANSWERS AND SOLUTION :
1(B)Explanation:
Let their investments be Rs. x for 14 months, Rs. y for 8 months and Rs. z for 7 months respectively.
Then, 14x : 8y : 7z = 5 : 7 : 8.
Now, 14x/8y  = 5/7  =>  98x = 40y   =>  y = 49/20 x
And, 14x/7z = 5/8 =>  112x = 35z    => z = 112/35 x = 16/5 .x.
So  x : y : z  =  x : 49/20 x : 16/5 x = 20 : 49 : 64.

2(D)Explanation :
The ratio of their initial investment = 1/2 : 1/3 : 1/4
= 6 : 4: 3
Let's take the initial investment of P, Q and R as 6x, 4x and 3x respectively
A:B:C = (6x * 2 + 3x * 10) : 4x*12 : 3x*12
= (12+30) : 4*12 : 3*12
=(4+10) : 4*4 : 12
= 14 : 16 : 12
= 7 : 8 : 6
B's share = 378 * (8/21) = 18 * 8 = 144

3(D)Explanation:
Let C = x.
Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000.
So, x + x + 5000 + x + 9000 = 50000
=> 3x = 36000
=> x = 12000
A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12.
So  A's share = Rs. (35000 x 21/50) = Rs. 14,700.

4(C)Explanation :
P:Q:R = (25*1+35*2) : (35*2 : 25*1) : (30*3)
= 95 : 95 : 90
= 19 : 19: 18

5(A)Explanation:
A : B : C = (20,000 x 24) : (15,000 x 24) : (20,000 x 18) = 4 : 3 : 3.
So  B's share = Rs. (25000 x 3/10) = Rs. 7,500.

6(C)Explanation :
Assume that investment of C = x
Then, investment of A =2x
Investment of B = 4x/3
A:B:C = 2x : 4x/3 : x = 2 : 4/3 : 1 =6 : 4 : 3
B's share = 157300 * 4/(6+4+3) = 157300*4/13
= 12100*4 = 48400

6(A)Explanation:
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.

7(D)Explanation :
Let P's capital = p, Q's capital = q and R's capital = r
Then
4p = 6q = 10r
=> 2p = 3q = 5r
=>q = 2p/3
r = 2p/5
P : Q : R = p : 2p/3 : 2p/5
= 15 : 10 : 6
R's share = 4650 * (6/31) = 150*6 = 900

8(C)Explanation :
Suppose C's capital = x then
B's capital = 4x (Since B's Capital is four times C's capital)
A's capital = 6x ( Since twice A's capital is equal to thrice B's capital)
A:B:C =6 x : 4x : x
= 6 : 4 : 1
B's share = 16500 * (4/11) = 1500*4 = 6000

9(C)Explanation :
Let the amount invested by Q = q
40000 : q = 2 : 3
=> 40000/q = 2/3
=> q = 40000 * (3/2) = 60000

10(A)Explanation:
Now as per question, Kamal invested for 12 months and Sameer invested for 7 months.
So  Kamal: Sameer = (9000*12):(8000*7)
= 108 : 56
=  27 : 14
Sameer Ratio in profit will be  =(6970*14/41)=Rs2380