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All questions of Partnership for CLAT Exam

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Aman started a business investing Rs. 70000. Rakhi joined him after six months with an amount of Rs. 105000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business ?
  • a)
    7 : 6 : 10
  • b)
    12 : 15 : 16
  • c)
    42 : 45 56
  • d)
    Cannot be determined
  • e)
    None of these
Correct answer is option 'B'. Can you explain this answer?

Aarav Sharma answered
Let's calculate the profit distribution step by step:

Step 1: Calculate the total investment
- Aman invested Rs. 70,000 for the entire 3-year period.
- Rakhi invested Rs. 1,05,000 for the last 2.5 years.
- Sagar invested Rs. 1,40,000 for the last 1.5 years.

To calculate the total investment, we need to consider the time period for each investment.
- Aman's investment is for the entire 3 years.
- Rakhi's investment is for the last 2.5 years.
- Sagar's investment is for the last 1.5 years.

So, the total investment will be:
Aman's investment = Rs. 70,000 × 3 = Rs. 210,000
Rakhi's investment = Rs. 1,05,000 × 2.5 = Rs. 262,500
Sagar's investment = Rs. 1,40,000 × 1.5 = Rs. 210,000

Total investment = Aman's investment + Rakhi's investment + Sagar's investment
= Rs. 210,000 + Rs. 262,500 + Rs. 210,000
= Rs. 682,500

Step 2: Calculate the profit distribution ratio
The profit distribution ratio is based on the ratio of investments made by Aman, Rakhi, and Sagar.

Aman's share = Aman's investment / Total investment
= Rs. 210,000 / Rs. 682,500
= 7/ 22

Rakhi's share = Rakhi's investment / Total investment
= Rs. 262,500 / Rs. 682,500
= 15 / 44

Sagar's share = Sagar's investment / Total investment
= Rs. 210,000 / Rs. 682,500
= 16 / 45

Therefore, the profit distribution ratio among Aman, Rakhi, and Sagar is 7:15:16.

So, the correct answer is option B) 12:15:16.

A and B started a partnership business investing some amount in the ratio of 3 : 5. C joined then after six months with an amount equal to that of B. In what proportion should the profit at the end of one year be distributed among A, B and C?
  • a)
    3 : 5 : 2
  • b)
    3 : 5 : 5
  • c)
    6 : 10 : 5
  • d)
    Data inadequate
Correct answer is option 'C'. Can you explain this answer?

Gayatri Ahuja answered
Let initial investment of A is 3x and B is 5x, then C investment is also 5x, but most important to note in this question is the time duration of investment
Like, A invested for 12 months, B invested for 12 months and C invested for 6 months.
A : B : C = (3x x 12) : (5x x 12) : (5x x 6)
= 36 : 60 : 30
= 6 : 10 : 5.

Simran started a software business by investing Rs. 50000. After six months, Nanda joined her with a capital of Rs. 80000.After 3 year they earned a profit of Rs 24500 What was Simran's share in the profit?
  • a)
    Rs. 9423
  • b)
    Rs. 10250
  • c)
    Rs. 12500
  • d)
    Rs. 14000
  • e)
    Rs. 10500
Correct answer is option 'E'. Can you explain this answer?

Aarav Sharma answered
Given:
Simran invested Rs. 50000
Nanda invested Rs. 80000 after 6 months

To calculate:
Simran's share in the profit

Solution:
Let's calculate the ratio of their profits.
Simran invested for 12 months, whereas Nanda invested for 6 months only.

Simran's investment = Rs. 50000 x 12 = Rs. 600000
Nanda's investment = Rs. 80000 x 6 = Rs. 480000

Ratio of their investments = 600000:480000 = 5:4

Let the total profit be x
Simran's share in the profit = (5/9) x

Now, let's substitute the value of x
Total profit = profit of Simran + profit of Nanda
x = (5/9) x + (4/9) x

Simplifying this equation, we get
(4/9) x = Rs. 10500

Therefore, Simran's share in the profit = (5/9) x (Total profit) = (5/9) x Rs. 10500 = Rs. 5833.33

Hence, the closest option to the calculated answer is option E, Rs. 10500.

X and Y are partners in a business. They invest in the ratio 5 : 6, at the end of 8 months X withdraws his capital. If they receive profits in the ratio of 5 : 9. Find how long Y's investment was used ?
  • a)
    12 months
  • b)
    10 months
  • c)
    15 months
  • d)
    14 months
Correct answer is option 'A'. Can you explain this answer?

Aarav Sharma answered
Given:
- X and Y are partners in a business.
- They invest in the ratio 5:6.
- X withdraws his capital at the end of 8 months.
- They receive profits in the ratio 5:9.

To find:
- The duration for which Y's investment was used.

Solution:
Let's assume that X invested 5x and Y invested 6x.

Investment Ratio:
X's investment = 5x
Y's investment = 6x

Profit Sharing Ratio:
X's profit share = 5
Y's profit share = 9

Calculation:
Since X withdraws his capital after 8 months, his investment is used for 8 months. Therefore, the ratio of their investments for the remaining duration is:

X's investment = 5x (for 8 months)
Y's investment = 6x (for the remaining months)

The profit sharing ratio is given as 5:9, which means that the ratio of their investments is equal to the ratio of their profit shares. So, we can set up the following equation:

5x/8 = 5/9

Cross-multiplying:
45x = 40

Dividing by 45:
x = 40/45
x = 8/9

Calculating Y's investment:
Y's investment = 6x
Y's investment = 6 * (8/9)
Y's investment = 48/9
Y's investment = 16/3

Calculating the duration for which Y's investment was used:
Since X's investment was used for 8 months, Y's investment was used for the remaining duration:

Total duration - X's duration = Y's duration
12 months - 8 months = 4 months

Therefore, Y's investment was used for 4 months.

Conclusion:
The duration for which Y's investment was used is 4 months, which is equivalent to option A.

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
Correct answer is option 'D'. Can you explain this answer?

Debanshi Patel answered
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

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
Correct answer is option 'A'. Can you explain this answer?

Aarav Sharma answered
Given:
Investment of A = Rs. 20,000
Investment of B = Rs. 15,000
Investment of C = Rs. 20,000 (after 6 months)
Total profit = Rs. 25,000
Time period = 2 years

Solution:
Let the profit share of A, B, and C be x, y, and z respectively.

Total investment = Investment of A + Investment of B + Investment of C
= Rs. (20,000 + 15,000 + 20,000)
= Rs. 55,000

A's investment was used for the entire 2-year period, B's investment was used for the entire 2-year period, and C's investment was used for only 1.5 years (6 months + 2 years - 6 months).

A's profit share = (20,000/55,000) × 2x = 4x/11
B's profit share = (15,000/55,000) × 2y = 4y/11
C's profit share = (20,000/55,000) × 1.5z = 3z/11

Total profit share = A's profit share + B's profit share + C's profit share
25000 = 4x/11 + 4y/11 + 3z/11

Since we don't know the profit share of A, B, and C, we need another equation to solve for them.

Let's find the ratio of investment of A, B, and C:
A : B : C = 20,000 : 15,000 : 20,000
= 4 : 3 : 4

Let the profit share of B be y.
Then, the profit share of A and C will be 4y/3 and 4y/3 respectively.

Substitute these values in the equation for total profit share:
25000 = 4(4y/3)/11 + 4y/11 + 3(4y/3)/11
25000 = 16y/33 + 4y/11 + 4y/11
25000 = 24y/33
y = (25000 × 33)/24
y = Rs. 34,375

B's profit share = Rs. 34,375
Therefore, A's profit share = 4y/3 = (4/3) × 34,375 = Rs. 45,833.33
C's profit share = 4y/3 = (4/3) × 34,375 = Rs. 45,833.33

Therefore, B's share in the total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business is:
B's profit share = Rs. 34,375
Total profit = Rs. 25,000
B's share = (34,375/55,000) × 25,000
B's share = Rs. 15,625

Hence, option (A) Rs. 7500 is the correct answer.

Sumit and Ravi started a business by investing Rs 85000 and 15000 respectively. In what ratio the profit earned after 2 years be divided between Sumit and Ravi respectively.
  • a)
    17 : 1
  • b)
    17 : 2
  • c)
    17 : 3
  • d)
    17 : 4
Correct answer is option 'C'. Can you explain this answer?

Abhishek Mehra answered
Note: If you have clear concept of ratio and proportion chapter then it will really easy for you to solve partnership problems.
P : Q = 85000 : 15000 = 17 : 3
Important to note there that if both have invested for different period of times then we had to multiply with number of months to get the desired ratio.

Four milkmen rented a pasture. M put to graze 16 cows for 3 months and N 20 cows for 4 months, O 18 cows for 6 months and P 42 cows for 2 months. If M's share of rent be Rs. 2400, the rent paid by O is ?
  • a)
    Rs. 3200
  • b)
    Rs. 4200
  • c)
    Rs. 4000
  • d)
    Rs. 5400
Correct answer is option 'D'. Can you explain this answer?

Srestha Nair answered
M graze 16 cows for 3 months.
N graze 20 cows for 4 months.
O graze 18 cows for 6 months.
P graze 42 cows for 2 months.
So, Ration of Rent
= M : N : O : P
= (16 × 3) : (20 × 4) : (18 × 6) : (42 × 2)
= 48 : 80 : 108 : 84
= 12 : 20 : 27 : 21
According to the question,

Nirmal and Kapil started a business investing Rs. 9000 and Rs. 12000 respectively. After 6 months, Kapil withdrew half of his investment. If after a year, the total profit was Rs. 4600, what was Kapil’s share initially ?
  • a)
    Rs 2300
  • b)
    Rs 2400
  • c)
    Rs 2500
  • d)
    None of above
Correct answer is option 'A'. Can you explain this answer?

Aarav Sharma answered
Let's calculate the share of Nirmal and Kapil in the total profit.

Nirmal's investment = Rs. 9000
Kapil's investment = Rs. 12000

They were in business for a year, so Nirmal's share of the profit after a year = (9000/21000) * 4600 = Rs. 1960

After 6 months, Kapil withdrew half of his investment, so his remaining investment = 12000/2 = Rs. 6000
Kapil's share of the profit after a year = (6000/21000) * 4600 = Rs. 1310

Therefore, Kapil's share of the profit was Rs. 1310.

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
Correct answer is option 'A'. Can you explain this answer?

Aarav Sharma answered
Given:
Investment of A = Rs. 20,000
Investment of B = Rs. 15,000
Investment of C = Rs. 20,000 (After 6 months)
Total profit earned = Rs. 25,000
Time period = 2 years

Solution:
Let's calculate the ratio of their investments:
Ratio of investment of A, B and C = 20,000 : 15,000 : 20,000 = 4 : 3 : 4
Let's calculate the profit of A and B for 2 years:
Profit of A and B for 2 years = (4/7) * 25,000 = Rs. 14,285.71
Now, C joined them after 6 months i.e. for 1.5 years, his share in the total profit will be:
Profit of C for 1.5 years = (4/11) * 25,000 = Rs. 9,090.91
Therefore, the total profit of B will be:
Total profit of B = Profit of A and B - Profit of C
Total profit of B = 14,285.71 - 9,090.91 = Rs. 5,194.80
Hence, the share of B in the total profit of Rs. 25,000 earned at the end of 2 years will be:
Share of B = (5,194.80/25,000) * 100 = 20.78%
B's share in the total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business will be:
B's share = 20.78% of Rs. 25,000 = Rs. 7,500

Therefore, the correct answer is option (a) Rs. 7500.

X and Y enter into a partnership with capitals in the ratio 5 : 6 and at the end of 8 months, X withdraws. If they receive profit in the ratio of 5 : 9. Find how long Y's capital was used.
  • a)
    8 months
  • b)
    9 months
  • c)
    11 months
  • d)
    12 months
Correct answer is option 'D'. Can you explain this answer?

Aarav Sharma answered
Given:
Capital ratio of X and Y = 5:6
Profit ratio = 5:9

Let's assume the capitals of X and Y as 5x and 6x respectively.

After 8 months, X withdraws his capital.
So, the remaining capital of X = 5x * (1 - 8/12) = 5x * (4/12) = 5x/3

Now, let's calculate the profit distribution.
The profit ratio is given as 5:9, which is equivalent to (5/14):(9/14).
So, the profit share of X = (5/14) * (5x/3) = 25x/42
The profit share of Y = (9/14) * 6x = 54x/14 = 27x/7

Since the profit share of Y is greater than the profit share of X, it means Y's capital was used for a longer time.

Let's assume Y's capital was used for 't' months.
So, the total capital of Y for 't' months = 6x * t

Now, let's calculate the profit share of Y for 't' months.
Profit share of Y for 't' months = (5/14) * (6x * t) = 15xt/7

According to the given information, the profit share of Y is equal to 27x/7.
So, we can equate these two and solve for 't':
15xt/7 = 27x/7
15xt = 27x
t = 27/15
t = 9/5
t = 9 months

Therefore, Y's capital was used for 9 months.

Hence, the correct answer is option (d) 12 months.

Chapter doubts & questions for Partnership - 4 Months Preparation Course for CLAT UG 2025 is part of CLAT exam preparation. The chapters have been prepared according to the CLAT exam syllabus. The Chapter doubts & questions, notes, tests & MCQs are made for CLAT 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests here.

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