Partnership MCQ Quiz - Objective Question with Answer for Partnership - Download Free PDF

Let initial investments be::

X = 4a

Y = 7a

Z = 6a

Time for each partner:

X and Z kept full investment for 12 months

Y invested 7a for 6 months, then reduced his investment

Y's remaining capital after 6 months:

Combined capital of X and Z = 4a + 6a = 10a

1/3 of that = (1/3) × 10a = 10a ÷ 3

So, Y invested 10a ÷ 3 for the remaining 6 months

Calculate effective capital × time (investment months):

X: 4a × 12 = 48a

Z: 6a × 12 = 72a

Y: 7a × 6 = 42a, and (10a ÷ 3) × 6 = 60a ÷ 3 = 20a

Total for Y = 42a + 20a = 62a

Total profit ratio:

X : Y : Z = 48a : 62a : 72a

⇒ Divide by 2: 24 : 31 : 36

Total parts = 24 + 31 + 36 = 91

Total Profit = ₹19,500

⇒ Y's share = (31 ÷ 91) × 18200 = ₹6,200

Thus, the correct answer is Rs. 6,200.

Given:

Total profit = ₹3,180

Investment ratio of X : Y : Z = 6 : 59 : 41

Formula used:

Profit share = (Individual investment ratio / Total ratio) × Total profit

Calculation:

Total ratio = 6 + 59 + 41 = 106

Profit share of Y = (59 / 106) × 3180

⇒ Profit share of Y = ₹1,770

Profit share of Z = (41 / 106) × 3180

⇒ Profit share of Z = ₹1,230

Difference between share of Y and Z = ₹1,770 - ₹1,230

⇒ Difference = ₹540

∴ The correct answer is option (1).

Given:

Investment of Alok = ₹56,000

Investment of Gita = ₹52,000

Investment of Suresh = ₹69,000

Total profit earned = ₹76,700

Charity = 31% of the total profit

Remaining profit = Total profit - Charity

Profit sharing ratio = Ratio of investments (Alok : Gita : Suresh)

Formula Used:

Charity = (31 / 100) × Total profit

Remaining profit = Total profit - Charity

Suresh's share = (Suresh's investment / Total investment) × Remaining profit

Calculation:

Charity = (31 / 100) × ₹76,700

⇒ Charity = ₹23,777

Remaining profit = ₹76,700 - ₹23,777

⇒ Remaining profit = ₹52,923

Total investment = ₹56,000 + ₹52,000 + ₹69,000

⇒ Total investment = ₹1,77,000

Profit sharing ratio (Alok : Gita : Suresh) = 56,000 : 52,000 : 69,000

⇒ Profit sharing ratio = 56 : 52 : 69

Suresh's share = (69 / (56 + 52 + 69)) × ₹52,923

⇒ Suresh's share = (69 / 177) × ₹52,923

⇒ Suresh's share = ₹20,631

Suresh's share is ₹20,631.

Given:

A invests ₹5000 initially, increases to ₹5500 after 3 months

B invests ₹3000 initially, increases by ₹y after 6 months (i.e., at the end of 6 months)

Profit ratio A : B = 43 : 40

Formula used:

Profit ∝ Investment × Time

Calculations:

A's investment:

₹5000 for 3 months = 5000 × 3 = 15000

₹5500 for 9 months = 5500 × 9 = 49500

Total = 64500

B's investment:

₹3000 for 9 months = 3000 × 9 = 27000

₹(3000 + y) for 3 months = (3000 + y) × 3 = 9000 + 3y

Total = 27000 + 9000 + 3y = 36000 + 3y

Profit ratio:

64500 : (36000 + 3y) = 43 : 40

⇒ 21500 : (12000 + y) = 43 : 40

⇒ 21500 / (12000 + y) = 43 / 40

⇒ 40 × 21500 = 43 × (12000 + y)

⇒ 860000 = 516000 + 43y

⇒ 344000 = 43y

⇒ y = 8000

⇒ 5y = 5 × 8000 = 40000

∴ The value of 5y is ₹40,000

Calculation

P and Q start a business.

P's investment is ₹2000 more than Q's.

P invests for 8 months, Q for 12 months.

Total profit at the end of the year = ₹6300.

Profit share of P is 16x, where

x=152 – 50 = 225 – 50 = 175

So, P's share = 16 × 175 =₹2800

Total profit = 6300

⇒Q’s share = 6300 – 2800 =3500

Let investment of Q = ₹y

→ Then P’s investment = ₹(y + 2000)

So:

P = (y+2000) ×8

Q = y×12y

Profit ratio = P : Q = 2800 : 3500 = 4 : 5

So:

[ (y+2000) × 8 ]/ 12y = 4/5

So, [(5 × 8) (y + 2000)] = 4 × 12y

⇒ 40y + 80000 = 48y

⇒ 80000 = [48y − 40y] = 8y

⇒ y = 80000/8 = 10,000

Investment of Q = 10,000

Given:

A invested Rs. 29,000, while B and C invested Rs. 25,000 each

After 4 months, A withdrew Rs. 3,000

After 6 months from the initial date, C invested Rs. 12,000 more to the business

The total profit = Rs. 33200

Calculation:

The ratio of A, B, and C = [(29000 × 4) + (26000 × 8)] : (25000 × 12) : [(25000 × 6) + (37000 × 6)]

= (116000 + 208000) : 300000 : (150000 + 222000)

= 324000 : 300000 : 372000

= 27 : 25 : 31

∴ The profit of C = (31/83) × 33200 = Rs. 12400

∴ The share of C( in Rs.) in the profit at the end of the year is Rs. 12400

Given:

A sum of 12540 is divided among A, B, and C.

Calculation:

Share of A = \(\dfrac{3}{10}\times 12540 = 3762\)

Share of B = \(\dfrac{2}{11}\times 12540 = 2280\)

Share of C = 12540 - (3762 + 2280) = 6498

∴ The share of C is Rs. 6498.

Given:

Peter started a retail business by investing Rs. 25000 

After eight months Sam joined him with a capital of Rs 30,000. 

After 2 years they earned a profit of Rs 18000

Concept Used:

The ratio of profit is equal to the ratio of the product of capital and time

Calculation:

The time period of Peter = 24 months

The time period of Sam = 16 months

Now,

25000 × 24 : 30000 × 16 = 5 : 4

∴ Peter’s share = (5/9) × 18000 = Rs. 10,000

Given:

Person A started a business by investing Rs. 65,000.

After a few months, B joined him by investing Rs. 50,000.

Three months after the joining of B, C joined the two with an investment of Rs. 55,000.

A got 50% of profit as his share.

Formula used:

Profit ratio = Investment1 × Time₁ : Investment₂ × Time₂ : ........... Investment_n × Time_n

Calculation:

Let B invest the amount after x months

A invest for 12 month

B invest for (12 - x)

​⇒ (12 - x) months

Three months after the joining of B, C joined the two with an investment of Rs. 55,000.

C invest for (12 - x - 3)

⇒ (9 - x)

Profit share = A : B : C

Profit share = 65,000 × 12 : 50,000 × (12 - x) : 55,000 × (9 - x)

⇒ 156 : 10(12 - x) : 11(9 - x)

A got 50% of profit as his share

⇒ 156/(156 + 120 - 10x + 99 - 11x) = 1/2

⇒ 312 = 375 - 21x

⇒ 21x = 63

⇒ x = 3 month 

∴ A alone finance the business for 3 month.

Given :

The ratio of investments of A  B and C = 3 : 2 : 6

After 6 months C withdraws half of his capital

Total profit earned in the year = Rs. 53010

Concept:

Investment = Capital x Duration of investment (in months)

Ratio of profits = Ratio of investments around 1 year

Calculation :

Let, the initial capital of A, B and C be 3a, 2a, and 6a

Now, Investment of A for 1 year = 12 x 3a = 36a

Investment of B for 1 year = 12 x 2a = 24a

According to the given data, C invested 6a for the first 6 months and 3a for the next 6 months.

Investment of C for 1 year = 6 x 6a + 6 x 3a = 54a 

Now, Ratio of their profits = 36a : 24a : 54a = 6 : 4 : 9

∴ Profit made by A = \(\dfrac{6}{6+4+9}× 53010 \)

⇒ \(\dfrac{6}{19}\) × 53010 = Rs. 16740

∴ The profit made by A is Rs. 16740.

Shortcut TrickRatio of their profits = \(12× 3:12×2:6(6+3) = 6:4:9\)

Profit of A = \(\dfrac{6}{19}× 53010 = 16740\)

Mistake Points According to the given data, C invested his initial amount for 6 months and after that, he withdrew half of his initial amount.

Given:

A, B, and C invested ₹40000, ₹48000, and ₹80000, respectively

The total profit = ₹ 672000

Calculation:

After six months, for the remaining time of the year, A added ₹4000, B added ₹4000 and C withdrew ₹4000 every month.

So, (4000 × 6) + (4000 × 5) + (4000 × 4) + (4000 × 3) + (4000 × 2) + (4000 × 1) = 4000 × 21 = 84000

A : B : C = [(40000 × 12) + 84000] : [(48000 × 12) + 84000] : [(80000 × 12) - 84000]

= (480000 + 84000) : (576000 + 84000) : (960000 - 84000)

= 564000 : 660000 : 876000

= 564 : 660 : 876

The share of C = [876/(564 + 660 + 876)] × 672000

= (876/2100) × 672000

= 280320

∴ C's share is ₹ 280320

Calculation:

Total capital invested by A = 60,000 × 12 + 90,000 × 12 = 720,000 + 1,080,000 = Rs 1,800,000

Total capital invested by B = 80,000 × 9 + 75,000 × 12 = 720,000 + 900,000 = Rs 1,620,000

Ratio = 1,800,000 : 1,620,000 = 10 : 9

Let the total profit earned is 4p

Now, out of 4p profit, 2p is equally divided between A and B.

A's profit-

⇒ p + \(10 \over 19\) × 2p = 35,880

⇒ 39p = 35,880 × 19

⇒ p = 35,880 × \(19\over 39\) = Rs 17,480

Now,Profit earned by B = p + \(9 \over 19\) × 2p  = \(37p\over 19\) = \(37\over 19\) × 17,480

⇒ Profit of B = Rs 34,040.

∴ The profit of B is Rs 34,040.

Given:

X, Y and Z started their business by investing ₹40,000, ₹38,000 and ₹30,000

Concept Used:

Profit = Amount of Investment × Time of Invest

Calculation:

Investment at the end of the year of X = 40000 × 6 + 60000 × 6 = 240000 + 360000

⇒ 600000

Investment at the end of the year of Y = 38000 × 6 + 30000 × 6 = 228000 + 180000

⇒ 408000

Investment at the end of the year of Z = 30000 × 6 + 45000 × 6 = 180000 + 270000

⇒ 450000

Ratio of profit share ratio = 600000 : 408000 : 450000

⇒ 100 : 68 : 75

Share of Y = 38880 × (68/243)

⇒ 10880

∴ The share of Y (in ₹) in the total profit of ₹38,880 made at the end of the year is 10880.

Given:

Three partners shared the profit in a business in the proportion of 9 ∶ 8 ∶ 11. They invested their capital for 4 months, 6 months, and 18 months, respectively. 

Concept used:

Profit is shared according to the capital invested.

Total investment = Invested Capital × Time period of the investment

Calculation:

Let the invested capital by them be P, Q, and R respectively.

According to the concept,

(P × 4) : (Q × 6) : (R × 18) = 9 : 8 : 11

⇒ 4P : 6Q : 18R = 9 : 8 : 11

Equating individual terms we get,

4P = 9

⇒ P = 9/4

Similarly, Q = 8/6 & R = 11/18

Now, we get,

P : Q : R = 9/4 : 8/6 : 11/18

⇒ P : Q : R = 9/4 × 36 : 8/6 × 36 : 11/18 × 36 

⇒ P : Q : R = 81 : 48 : 22

∴ The ratio of their capitals is 81 : 48 : 22.

Given: 

Initial investment by A = ₹75,000

B joins 5 months later with an investment = ₹80,000

Total profit after 1 year = ₹4,08,800

Concept Used:

Profit shares ∝ (Investment × Time Period)

Calculations:

A's Capital-Time = ₹75,000 × 12 months = ₹9,00,000 months

B's Capital-Time = ₹80,000 × 7 months = ₹5,60,000 months

Ratio of A's and B's capital-time:

⇒ A : B = ₹9,00,000 : ₹5,60,000

⇒ A : B = 90 : 56

⇒ A : B = 45 : 28

Share of total profit according to ratio:

⇒ A's share = (45/(45+28)) × ₹4,08,800 = ₹2,52,000

⇒ B's share = (28/(45+28)) × ₹4,08,800 = ₹1,56,800

∴ A's share = ₹2,52,000 and B's share = ₹1,56,800.