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

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

Calculation:

Investments:

A: ₹4000 for n months

B: ₹6000 for n + 2 months

C: ₹5000 for 10 months

A's profit = ₹1600

Total profit = ₹6480

So, B and C together share ₹6480 – ₹1600 = ₹4880

Profits are divided in the ratio of:

Investment × Time

Let’s write the profit ratios:

A's share ∝ 4000 × n = 4000n

B's share ∝ 6000 × (n + 2)

C's share ∝ 5000 × 10 = 50000

So, total profit ratio:

A : B : C = 4000n : 6000(n + 2) : 50000

Let’s assume this ratio is proportional to their actual profit shares:

A’s share = ₹1600

Total = ₹6480

So, let's convert the ratios to actual values:

Let’s write the ratios in terms of A’s share = ₹1600

Let:

4000n = A's share → corresponds to ₹1600

Then 1 unit = ₹1600 / 4000n = ₹2/5n

Now find the other shares in terms of ₹:

B’s share = 6000(n+2) × (2 / 5n)

C’s share = 50000 × 2 / 5n

And total of B and C = ₹4880

So:

6000(n+2) × (2/5n) + 50000 × (2/5n) = 4880

Take LHS:

(2/5n) [6000 (n+2) + 50000] = 4880

First compute inside the bracket:

6000 (n+2) = 6000n + 12000 ⇒ 6000n + 12000 + 50000 = 6000n + 62000

Now:

(2/5n) 6000n + 62000 = 4880

Multiply both sides by 5n:

2 (6000n + 62000) = 4880 × 5n ⇒ 12000n + 124000 = 24400n

124000 = 24400n − 12000n = 12400n ⇒ n = 124000 / 12400 = 10

B invested for n + 2 = 10 + 2 = 12 months

Thus, the correct answer is 12 months.

Calculation:

Let Q's initial investment = y 

Then, P's initial investment = (y - 4,000) since P invested Rs. 4,000 less than Q

First 8 Months:

P's investment: y - 4,000

Q's investment: y 

After 8 Months for the remaining 4 months:

P withdraws Rs. 4,000:

New investment = (y - 4,000) - 4,000 = y - 8,000

Q adds Rs. 8,000:

New investment = y + 8,000

Profit share is based on the product of investment and time.

P's Total Investment:

(y - 4,000) × 8 + (y - 8,000) × 4 = 8y - 32,000 + 4y - 32,000 = 12y - 64,000

Q's Total Investment:

y × 8 + (y + 8,000) × 4 = 8y + 4y + 32,000 = 12y + 32,000

Given Profit Ratio P:Q = 1:4

(12y - 64,000) / (12y + 32,000) = 1 / 4

Solve for y:

4 (12y - 64,000) = 12y + 32,000

48y - 256,000 = 12y + 32,000

36y = 288,000 ⇒ y = 8000

P's Initial Investment: y - 4,000 = 8000 - 4,000 = 4000

Difference:

8000 - 4000 = 4000

Thus, the difference between initial investments is Rs. 4,000.

Given:

Investment by A = Rs. x

Investment by B = Rs. (x + 5000)

Profit share ratio of A to B = 7 : 9

Formula used:

Profit share ratio = Investment ratio (since profit is directly proportional to investment)

Calculations:

Let the total profit be P.

The ratio of profit shares of A and B is given as 7:9. So, the profit for A is 7 parts and for B is 9 parts.

The total parts = 7 + 9 = 16 parts.

The profit share of A and B is directly proportional to their investments.

Investment of A / Investment of B = Profit share of A / Profit share of B

So, x / (x + 5000) = 7 / 9

Cross multiplying:

9x = 7(x + 5000)

9x = 7x + 35000

9x - 7x = 35000

2x = 35000

x = 35000 / 2 = 17500

Now, find the value of 7x:

7x = 7 × 17500 = 122500

∴ The value of 7x is Rs. 122500.

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 = 

Share of B = 

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 = 

⇒  × 53010 = Rs. 16740

∴ The profit made by A is Rs. 16740.

Shortcut TrickRatio of their profits = 

Profit of A = 

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 +  × 2p = 35,880

⇒ 39p = 35,880 × 19

⇒ p = 35,880 ×  = Rs 17,480

Now,Profit earned by B = p +  × 2p  =  =  × 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 data:

Profit ratio = 5 : 9

Investment of B = Rs 36,000

Time for which B invested = 12

Time for which A invested = 8

Formula used:

Total profit = Investment × time

Calculation:

Total investment of A = A × 8

Total investment of B = 36,000 × 12 = 432,000

Ratio = 8A : 432,000

⇒  = 

⇒ A =  = Rs 30,000

∴ The total investment of A is Rs 30,000.