# Partnership Questions and Answers updated daily – Aptitude

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## Partnership Questions

81. 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?

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Correct Ans:Rs.2500/-

Explanation:

**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 : B's part= 25 :35**

Total --> 60 parts -----> Rs.6000/-

1 part ------> Rs.100/-

Then,

**A's share**= 25 parts = Rs.100/- * 25 parts =

**Rs.2500/-**

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82. 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, B joined the business after:?

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Correct Ans:7 Months

Explanation:

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 x d = b x c

=> 6 : 5 = 3 : 1

=> 3x = 15

=>

Then,

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 x d = b x c

**A**= 5000/- per 12 Months**B**= 4000/- per x Months 4000 * 12 : 5000 * 8 = 3 : 1=> 6 : 5 = 3 : 1

=> 3x = 15

=>

**x = 5 Months**Then,

**B**joined the**business after**= 12 - x ==> 12 - 5 ==>**after 7 Months.**
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83. 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?

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Correct Ans:5 Months

Explanation:

Let the number of months B in the business = x

Given, A's investment = Rs. 5000 for 12 months

B's investment = Rs. 4000 for x months

Given Profit ratio = 3 : 1

=>

=> 3 : 1 = (5000 * 12) : (4000 * x)

=> 3 : 1 = 15 : x

=> 3/1 = 15 / x

=> x = 15 / 3

=>

Given, A's investment = Rs. 5000 for 12 months

B's investment = Rs. 4000 for x months

Given Profit ratio = 3 : 1

=>

**Ratio of Profit = Ratio of investment**=> 3 : 1 = (5000 * 12) : (4000 * x)

=> 3 : 1 = 15 : x

=> 3/1 = 15 / x

=> x = 15 / 3

=>

**x = 5**

Thus,number of months B in the business = 5 monthsThus,number of months B in the business = 5 months

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84. 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:

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Correct Ans:9000

Explanation:

Given Profit is for one year = 12 months, so the peroid of given business = 12 months.

Given, A investment = Rs. 3500 for 12 months

Given, B joined the business after 5 months, which means he is in the business for (12 - 5) = 7 months.

Let

Given Profit Ratio = 2 : 3

=> (3500 * 12) : (x * 7) = 2 : 3

=> (500 * 12) / x = 2 / 3

=> x = (500 * 12) * 3/2

=> x = 500 * 6 * 3

=>

Therefore,

Given, A investment = Rs. 3500 for 12 months

Given, B joined the business after 5 months, which means he is in the business for (12 - 5) = 7 months.

Let

**B's contribution in the capital**=**Rs. "x"**Given Profit Ratio = 2 : 3

**A and B's Ratio of (Amount invested * No. of months in business) = A, B's Ratio of profit**=> (3500 * 12) : (x * 7) = 2 : 3

=> (500 * 12) / x = 2 / 3

=> x = (500 * 12) * 3/2

=> x = 500 * 6 * 3

=>

**x = 9,000**Therefore,

**B's contribution in the capital**=**Rs. "x" = Rs. 9,000**
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85. 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.

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Correct Ans:6:10:05

Explanation:

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

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

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86. 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?

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Correct Ans:80000

Explanation:

A:B:C = 27000:72000:81000

= 3:8:9

Let the total profit= p

Then p * 9/20 = 36000

=> p = 36000 * 20/9 = 80000

= 3:8:9

Let the total profit= p

Then p * 9/20 = 36000

=> p = 36000 * 20/9 = 80000

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87. 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

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Correct Ans:60000

Explanation:

Let the amount invested by Q = q

40000 : q = 2 : 3

=> 40000/q = 2/3

=> q = 40000 * (3/2) = 60000

40000 : q = 2 : 3

=> 40000/q = 2/3

=> q = 40000 * (3/2) = 60000

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88. A and B starts a business investing Rs.85,000 and Rs.15,000 respectively. Find out the ratio in which the profits should be shared.

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Correct Ans:17:3

Explanation:

Here A's and B's capitals are there for an equal time. Hence

= 85000 : 15000

= 85 : 15

=

**Ratio of share of profits between A and B**=A's investedamount :B's investedamount= 85000 : 15000

= 85 : 15

=

**17 : 3**
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89. A started a business by investing Rs.10000/-.After 1 year B joined by investing Rs.15000/- After 6 months C joined by investing Rs.24000/-. At the end of two years, they got a profit of Rs.47000/-. What is A's share?

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Correct Ans:Rs.20000/-

Explanation:

A = Rs.10000/- per 24 months

B = Rs.15000/- per 12 months

C = Rs.24000/- per 6 months

A : B : C = 10000 * 24 : 15000 * 12 : 24000 * 6

= 20 : 15 : 12

Total = 47 parts -----> Rs.47000/- (profit)

=> 1 part ------> Rs.1000/-

Then, A's share is

= 20 part = Rs.1000/- * 20 parts = Rs.20,000/-

B = Rs.15000/- per 12 months

C = Rs.24000/- per 6 months

A : B : C = 10000 * 24 : 15000 * 12 : 24000 * 6

= 20 : 15 : 12

Total = 47 parts -----> Rs.47000/- (profit)

=> 1 part ------> Rs.1000/-

Then, A's share is

= 20 part = Rs.1000/- * 20 parts = Rs.20,000/-

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90. 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?

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Correct Ans:Rs.3000/-

Explanation:

A = Rs.5000/- per 12 months

B = Rs.4000/- per 8 months

C = Rs.3000/- per 6 months

A : B : C= (5000 * 12) : (4000 * 8) : (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/-

B = Rs.4000/- per 8 months

C = Rs.3000/- per 6 months

A : B : C= (5000 * 12) : (4000 * 8) : (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/-

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91. A started a business by investing Rs.4000/-. After 4 months B joined by investing Rs.5000/- At the end of the year, there was a profit of Rs.8800/-. What is A's share?

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Correct Ans:Rs.4800/-

Explanation:

A = Rs.4000/- per 12 months
B = Rs.5000/- per 8 months

= 4000 * 12 : 5000 * 8 = 6 : 5 Total = 11 parts -----> Rs.8800/- (profit)

= 1 part ------> Rs.800/-

Then, A's share is

= 6 part = Rs.800/- * 6 parts = Rs.4800/-

= 4000 * 12 : 5000 * 8 = 6 : 5 Total = 11 parts -----> Rs.8800/- (profit)

= 1 part ------> Rs.800/-

Then, A's share is

= 6 part = Rs.800/- * 6 parts = Rs.4800/-

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92. A,B and C started a business in which A invested Rs.2000/- for 1 year, 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?

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Correct Ans:Rs.8000/-

Explanation:

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/-

= 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/-

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93. A,B and C started a business in which A invested Rs.20000/- for 2 year, 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 Bï¿½s share?

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Correct Ans:Rs.3600/-

Explanation:

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/-

=> 400 * 9 parts = Rs.3600/-

= 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/-

=> 400 * 9 parts = Rs.3600/-

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94. 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?

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Correct Ans:4

Explanation:

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, and joined after 12-8 = 4 months

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, and joined after 12-8 = 4 months

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95. 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?

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Correct Ans:48400

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

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

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96. 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

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Correct Ans:900

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

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

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97. 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?

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Correct Ans:144

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

P:Q:R = (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

= 6 : 4: 3

Let's take the initial investment of P, Q and R as 6x, 4x and 3x respectively

P:Q:R = (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

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98. A,B and C started a business in which A invested Rs.10000/- for 1 year, B invested Rs.20000/- for 2 years, C invested Rs.30000/- for 3 years. At the end, the profit received by them is Rs.5600/-. What is C's share?

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Correct Ans:Rs.3600/-

Explanation:

Given,A invested Rs.10,000/- for 1 year, B invested Rs.20,000/- for 2 years, C invested Rs.30,000/- for 3 years.

Therefore, the ratio of investment of A, B, C = Ratio of (Amount invested * No. of months in Business)

= (10,000 * 12) *: (20,000 * 24) : (30,000 * 36)

= (1 * 12) : (2 * 24) : (3 * 36)

= 1 : 4 : 9

Thus,Total parts of share = 1 + 4 + 9 = 14

C's part of share = 9

Given,total profit = Rs. 5600

Hence, C's share = Rs. (9/14) * 5600 =

Therefore, the ratio of investment of A, B, C = Ratio of (Amount invested * No. of months in Business)

= (10,000 * 12) *: (20,000 * 24) : (30,000 * 36)

= (1 * 12) : (2 * 24) : (3 * 36)

= 1 : 4 : 9

Thus,Total parts of share = 1 + 4 + 9 = 14

C's part of share = 9

Given,total profit = Rs. 5600

Hence, C's share = Rs. (9/14) * 5600 =

**Rs. 3600**
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99. A,B started a business in which A invested Rs.10000/- for 1 year, B invested Rs.20000/- for 2 years. At the end of the profit received by them is Rs.5000/-. What is A's share?

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Correct Ans:Rs.1000/-

Explanation:

A = Rs.10000/- per 1 year
B = Rs.20000/- per 2 years

= 10000 * 1 : 20000 * 2 = 1 : 4 Total = 5 parts -----> Rs.5000/- (profit)

= 1 part ------> Rs.1000/-

Then, A's share is

= 1 part = Rs.1000/-

= 10000 * 1 : 20000 * 2 = 1 : 4 Total = 5 parts -----> Rs.5000/- (profit)

= 1 part ------> Rs.1000/-

Then, A's share is

= 1 part = Rs.1000/-

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100. A,B and C started a business by investing Rs.1400/- , Rs.4200/- and Rs.7000/- respectively. Total profit is Rs.8100/-. Find the C's share?

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Correct Ans:Rs.4500/-

Explanation:

Ratio of investment of A, B and C = 1400 : 4200 : 7000

= 1 : 3 : 5

Given,

Then, C's share = 5/ (1 + 3 + 5) * 8100

= (5 /9) * 8100

= Rs. 4500

= 1 : 3 : 5

Given,

**Total profit = Rs.8100**Then, C's share = 5/ (1 + 3 + 5) * 8100

= (5 /9) * 8100

= Rs. 4500

**=> C's share =Rs. 4500**
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