Partnership : Aptitude Test

1.

A began a business with Rs,5000/- and was joined afterwards by B with Rs.4000/-. If the profits at the end of the year were divided in the ratio 3:1, How many months B was in the business?

   A.) 4 Months
   B.) 7 Months
   C.) 5 Months
   D.) 6 Months

Answer: Option 'C'

Note : 
1) Share's ratio is always equal to profit ratio
2) When two ratios are equal, then the cross products of the ratios are equal. 
That is, for the proportion, a:b = c:d , a × d = b × c 
A = Rs.5000/- per 12 Months
B = Rs.4000/- per x Months 
4000 × 12 : 5000 × 8 = 3 : 1 
=> 6 : 5 = 3 : 1  
=> 3x = 15 
=> x = 5 Months 
 

2.

Suresh started a business with Rs.20,000. Kiran joined him after 4 months with Rs.30,000. After 2 months, Suresh withdrew Rs.5,000 of his capital and 2 more months later, Kiran brought in Rs.20,000 more. What should be the ratio in which they should share their profits at the end of the year?

   A.) 21:32
   B.) 21:22
   C.) 32:21
   D.) 32:21

Answer: Option 'A'

Here capital is not the same. 
Suresh invest 20000 for initial 6 months and 15000 for the next 6 months. 
Hence his term of ratio 
=( 20000 × 6 + 15000 × 6) 
Kiran invest Rs.30000 for 4 months and Rs.50000 for next 4 months. 
Hence his term of ration 
= (30000 × 4 : 50000 × 4) 
Suresh : Kiran = ( 20000 × 6 + 15000 × 6) : (30000 × 4 : 50000 × 4) 
= (20 × 6 + 15 × 6) : (30 × 4 + 50 × 4) 
= (20 × 3 + 15 × 3) : (30 × 2 : 50 × 2) 
= 105:160 
= 21:32

3.

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.) 48600
   B.) 48400
   C.) 48500
   D.) 44800

Answer: Option 'B'

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

4.

A,B and C started a business in which A invested Rs.2000/- for 1year, B invested Rs.3000/- for 1 1/2 years, C invested Rs.4000/- for 2 years. At the end of the profit received by them is Rs.14500/-. What is C’s share? 

   A.) Rs.2000/-
   B.) Rs.4500/-
   C.) Rs.8000/-
   D.) Rs.1600/-

Answer: Option 'C'

A = Rs.20000/- per 12 months
B = Rs.30000/- per 18 months 
C = Rs.40000/- per 24 months 
= 20000 × 12 : 30000 × 18 : 40000 * 24 
= 4 : 9 : 16 
Total = 29 parts -----> Rs.14500/- (profit)  
         = 1 part ------> Rs.500/- 
Then, C's share is  
         = 16 part = Rs.500/- × 16 parts = Rs.8000/- 

5.

In a business A invested 1/3rd of total investment in 1/3rd of period of invested, B invested 1/4th of total investment in 1/4th of period of investment and remaining was invested by C in remaining period. Then the ratio’s between their shares is:

   A.) 25:9:16
   B.) 9:25:16
   C.) 16:9:25
   D.) 25:16:9

Answer: Option 'C'

share's ratio = A : B : C = 4 : 3 : 5 
=Time ratio == A : B : C = 4 : 3 : 5 
=profit ratio = A : B : C = 16 : 9 : 25 

6.

A and B started a partnership business investing capital in the ratio of 3 : 5. C joined in the partnership after six months with an amount equal to that of B. At the end of one year, the profit should be distributed among A, B and C in --- proportion. 

   A.) 6 : 10 : 5
   B.) 10 : 5 : 4
   C.) 3 : 4: 5
   D.) 9 : 5 : 4

Answer: Option 'A'

Initial investment capital ratio of A and B = 3 : 5
Hence we can assume that initial capital of A and B are 3x and 5x respectively.
Amount that C invest after 6 months = 5x (Since it is equal to B's investment)
Ratio in which profit should be distributed after 1 year = 3x × 12 : 5x × 12 : 5x × 6
=> 3 × 12 : 5 × 12 : 5 × 6 
= 6 : 10 : 5

7.

A starts a business with a capital of Rs. 85,000. B joins in the business with Rs.42500 after some time. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1?

   A.) 5 months
   B.) 8 months
   C.) 7 months
   D.) 6 months

Answer: Option 'B'

Let B joins for x months. Then
A:B = 85000 × 12 : x × 42500 = 3 : 1
=> 850 × 12 : 425x= 3 : 1
=> 850 × 12/ 425x = 3/1 = 3
=> 850 × 4 /425x = 1
=> 2 × 4/x = 1
=> x = 8

8.

Kamal started a business with Rs.25000 and after 4 months, Kiran joined him with Rs.60000. Kamal received Rs.58000 including 10% of profit as commission for managing the business. What amount did Kiran receive?

   A.) 72000
   B.) 70000
   C.) 70200
   D.) 72200

Answer: Option 'C'

Ratio of the profits = 25000 × 12 : 60000 × 8
= 25 × 12 : 60 × 8 = 5 × 3 : 12:2 = 5 : 4 × 2 
= 5:8
Let the total profit = x. 
Then Kamal received 10x/100 = x/10 as commission for managing the business
Remaining profit = x- x/10 = 9x/10 which is shared in the ration 5:8
Kamal's share = x/10 + (9x/10) × (5/13) = 58000
=> x + 9x(5/13) = 580000
=> x(1 + 45/13) = 580000
=> x ( 58/13) = 580000
=> x ( 1/13) = 10000
=> x = 130000
Kiran's share = 130000 - 58000 = 72000

9.

A,B invested Rs.20,000/- and Rs.25,000/- respectively in a business. The 20% of profits goes to charities. The rest being divided in proportion to their capitals out of a total profit of Rs.9000/-. The A’s share is:

   A.) Rs.4000/-
   B.) Rs.5000/-
   C.) Rs.3200/-
   D.) Rs.3600/-

Answer: Option 'C'

A = Rs.20,000/- & B = Rs.25,000/- 
==> A : B = 20 : 25 
==> 4 : 5 
Total profit = Rs.9000/-
20 % of prifit goes to charities ===> Rs.9000/- - Rs.1800/- = Rs.7200/- 
remaining amount = Rs.7200/- 
Total parts = 9 
9 parts -----> Rs.7200/-
1 part ------> Rs.800/- 
A's share ===> Rs.800/- × 4 parts = Rs.3200/-

10.

A, B and C rent a pasture. A grazed his 35 cows for 20days, B grazed his 20 cows for 30 days and C grazed his 30 cows for 15 days. If A paid Rs. 1050 as rent , find the rent paid by them.

   A.) Rs. 1650/-
   B.) Rs. 2625/-
   C.) Rs. 2735/-
   D.) Rs. 2135

Answer: Option 'B'

Let the rent per cow per day be Rs.x
A's rent = 34 × 20x
700x = 1050
x = 1.5
Total rent = 1050 + 600x + 450x = 1050 + 900 + 675 = Rs. 2625/-

11.

A and B invest in a business in the ratio 3: 2. Assume that 5% of the total profit goes to charity. If A's share is Rs. 855, what is the total profit?

   A.) 1400
   B.) 1200
   C.) 1500
   D.) 1600

Answer: Option 'C'

Assume that the total profit is x. 
Since 5% goes for charity, 95% of x will be divided between A and B in the ratio 3: 2
=> A's profit = (95x/100) × (3/5) = 855
=> 95x/100 = 855 × 5/3 = 285 × 5 = 1425
=> x = 1425 × 100/95 = 285 × 100/19 = 1500 
Hence the total profit = 1500

12.

A,B invested Rs.20,000/- and Rs.25,000/- respectively in a business. The 20% of profits goes to charities. The rest being divided in proportion to their capitals out of a total profit of Rs.9000/-. The A’s share is:

   A.) Rs.4000/-
   B.) Rs.5000/-
   C.) Rs.3200/-
   D.) Rs.3600/-

Answer: Option 'C'

A = Rs.20,000/- & B = Rs.25,000/- 
==> A : B = 20 : 25 
==> 4 : 5 
Total profit = Rs.9000/-
20 % of prifit goes to charities ===> Rs.9000/- - Rs.1800/- = Rs.7200/- 
remaining amount = Rs.7200/- 
Total parts = 9 
9 parts -----> Rs.7200/-
1 part ------> Rs.800/- 
A's share ===> Rs.800/- × 4 parts = Rs.3200/-

13.

A,B started a business by investing Rs.10000/- and Rs.20000/- respectively. After 1year B withdrew Rs.5000/- and A invested Rs.5000/- more. At the end of 2 years they got total Profit Rs.6000/-. What is A’s share?

   A.) Rs.3500/-
   B.) Rs.2800/-
   C.) Rs.2000/-
   D.) Rs.2500/-

Answer: Option 'D'

A's Share = Rs.10000/- per first 1 year, Next year Rs.5000/- added 
= Rs.10000/- × 1 + Rs.15000 × 1 = 25000 
B's Share = Rs.20000/- per first 1 year, Next year Rs.5000/- reduced 
= Rs.20000/- × 1 + Rs.15000/- × 1 = Rs.35000/- 
 Then,A's part= 25 : B's part= 35  
 Total 60 parts -----> Rs.6000/- 
            1 part ------> Rs.100/- 
Then, A's share is 
 25parts = Rs.100/- × 25 parts = Rs.2500/- 

14.

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

   A.) 7000
   B.) 9000
   C.) 10000
   D.) 6000

Answer: Option 'B'

Ratio in which profit is divided = 2:3
Assume that B's contribution to the capital = b
=> 3500 × 12 : b × 7 = 2:3
=> 3500 × 12/7b = 2/3
=> b = (3500 × 12 × 3)/(2 × 7) = 500 × 6 × 3 = 9000

15.

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

   A.) 44
   B.) 47
   C.) 46
   D.) 45

Answer: Option 'C'

A : B: C = 10 × 7 : 12 × 5 : 15 × 3 = 2 × 7 : 12 × 1 : 3 × 3 = 14 : 12 : 9
amount that C should pay = 175 × (9/35) = 5 × 9 = 45

16.

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.) 700
   B.) 900
   C.) 600
   D.) 750

Answer: Option 'B'

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

17.

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.11500/-
   C.) Rs.11000/-
   D.) Rs. 14,700

Answer: Option 'D'

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.
A's share = Rs. (35000 x 21/50) = Rs. 14,700.

18.

Ravi, Naresh and Raju started a business in which Ravi invested Rs. 18,000/-, Naresh  invested Rs. 22,000/ and Raju invested Rs. 30,000/-. At the end of the year profit received by them is Rs. 14,000/-. What is the difference between the profits Ravi and Raju?

   A.) Rs. 2500/-
   B.) Rs. 2400/-
   C.) Rs. 2300/-
   D.) Rs. 2100/-

Answer: Option 'B'

18000 : 22000 : 30000
    9    :  11  :  15
The difference between Ravi and Raju  15 - 9 = 6
total 35  --------> 14000
only  6 ---------> ?
(6/35) × 14,000 = 2400/-

19.

A,B and C started a business in which A invested Rs.20000/- for 2year, B invested Rs.30000/- for 3 years, C invested Rs.40000/- for 4 years. At the end of the profit received by them is Rs.11,600/-. What is B’s share? 

   A.) Rs.3600/-
   B.) Rs.6400/-
   C.) Rs.3200/-
   D.) Rs.3200/-

Answer: Option 'A'

A = Rs.20000/- per 2 year 
B = Rs.30000/- per 3 years 
C = Rs.40000/- per 4 years 
= 20000 × 2 : 30000 × 3 : 40000 × 4 
= 4 : 9 : 16 
Total = 29 parts -----> Rs.11600/- (profit)  
         = 1 part ------> Rs.400/- 
Then, B's share is 
         = 9 part = Rs.400/- × 9 parts = Rs.3600/- 

20.

A started a business by investing Rs.5000/-. After 4 months B joined by investing Rs.4000/- After 2 months C joined by investing Rs.3000/-. At the end of the year, they got a profit of Rs.5500/-. What is A’s share? 

   A.) Rs.900/-
   B.) Rs.1600/-
   C.) Rs.3600/-
   D.) Rs.3000/-

Answer: Option 'D'

A = Rs.5000/- per 12 months
B = Rs.4000/- per 8 months 
C = Rs.3000/- per 6 months 
= 5000 × 12 : Rs.4000 × 8 : Rs.3000 × 6 
= 30 : 16 : 9 
Total = 55 parts -----> Rs.5500/- (profit)  
        = 1 part ------> Rs.100/- 
Then, A's share is
        = 30 part = Rs.100/- × 30 parts = Rs.3000/-

21.

In a business, A,B inversed Rs.10,000/-,Rs.20,000/- respectively. After 4 months A adds Rs.5000/- to his initial investment and B withdrew Rs.5000/- from his initial investment. At the end of the year total amount of profit they got is Rs.5400/-. What is A’s share?

   A.) Rs.600/-
   B.) Rs.3000/-
   C.) Rs.4500/-
   D.) Rs.2400/-

Answer: Option 'D'

A's Share = Rs.10000/- per first 4 maonth + Next 8 months Rs.5000/- added 
= 10 × 4 + 15 × 8 = 40 + 120 = 160 
B's Share = Rs.20000/- per first 4 months + Next 8 months Rs.5000/- added 
= 20 × 4 + 15 × 8 = 200   
Then,A's part= 160 : B's part= 200 
==> 4 : 5 
 Total 9 parts -----> Rs.5400/- 
           = 1 part ------> Rs.600/- 
Then, A's share is 
= 25parts = Rs.600/- × 4 parts = Rs.2400/- 

22.

A invested Rs 76000 in a business. After few months, B joined him with Rs 57000. The total profit was divided between them in the ratio 2 : 1 at the end of the year. After how many months did B join?

   A.) 3
   B.) 4
   C.) 5
   D.) 6

Answer: Option 'B'

Answer: Option 'B' 
Assume that B joins for x months . Then
A : B = 76000 × 12 : 57000 × x = 2:1
=> 76 × 12 : 57x = 2:1
=> 76 × 12/57x = 2/1 = 2
=> x = 76 × 12/57 × 2 = 76 × 4/19 × 2 = 8
Hence B was there in the business for 8 months, or joined after 12-8 = 4 months

23.

A, B and C start a business with their investments in the ratio 3 : 2 : 1. A leaves after 6 months and B leaves after 9 months. Find the ratio of profits at the end of a year.

   A.) 2 : 2 : 3
   B.) 3 : 3 : 2
   C.) 3 : 2 : 3
   D.) 3 : 4 : 4

Answer: Option 'B'

Ratio of the profits = (3 × 6) : 2 × 9) : (1 × 12)
=> 18 : 18 : 12 = 3 : 3 : 2

24.

X and Y invest Rs.21000 and Rs.17500 respectively in a business. At the end of the year, they make a profit of Rs.26400. What is the share of X in the profit?

   A.) Rs.12000/-
   B.) Rs.12500/-
   C.) Rs.26400/-
   D.) Rs.14400/-

Answer: Option 'D'

Ratio of the investment = 21000 : 17500 = 210 : 175 = 42 : 35 = 6 : 5
Share of X in the profit = 26400 × (6/11) = 2400 × 6 = 14400

25.

A , B , C started a partnership business by investing Rs 27000 , 72000 , 81000 respectively. At the end of the year , the profit were distributed among them. If C's share of profit is 36000, What is the total profit? 

   A.) 80000
   B.) 90000
   C.) 70000
   D.) 110000

Answer: Option 'A'

A:B:C = 27000:72000:81000
= 3:8:9
Let the total profit= p
Then p × 9/20 = 36000
=> p = 36000 × 20/9 = 80000


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