Test: Partnership - 1 - UPSC MCQ

Since C is the sleeping partner and his share of profit will be half of what it would have been if he were a working partner
⇒ Ratio in which the profit will be shared = 4 ∶ 5 ∶ 7/2 = 8 : 10 : 7
Profit = 36000 and when 25% is reinvested then
Profit to be shared between A, B & C = 36000 × 0.75 = Rs. 27000
∴ B’s share = 10/25 × 27000 = Rs. 10800

Given
Kirti started the business = Rs. 10,000 
Suma joined the business = Rs. 30,000 

Formula 
Profit = Investment × time 

Calculation 
Let, Suma joined Kirti after X months
⇒ 10,000 × 12 = 30,000 × (12 - X)
⇒ 1,20,000 = 3,60,000 – 30,000X
⇒ 3,60,000 – 1,20,000 = 30,000X
⇒ 2,40,000 = 30,000X
⇒ X = 8 Months
∴ Suma joined kirti after 8 months.

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:
Jayesh started project with Rs. 6000
Due to some issue, project stuck for 2 months and after that due to financial issue it doesn’t progress more 4 months = (2 + 4) = 6 months
Dinesh helped Jayesh with Rs. 8000
The project generate the revenue in the end of the year = Rs. 20,000

Calculation:
Costing spend on Project = (6000 + 8000) = Rs. 14,000
Net profit = revenue – cost = (20,000 – 14,000) = Rs. 6,000
For the share of individual,
Jayesh’s investment × time period ∶ Dinesh’s investment × time period = 6000 × 12 ∶ 8000 × 6
⇒ Respected ratio = 3 ∶ 2
Now,
Share of Dinesh = [(2/5) × 6000] = Rs. 2400
∴ The share of profit of Dinesh is Rs. 2400.

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:
Three partners invested in the ratio 4 : 6 : 9 for 3 years, 1 year and 4 years respectively. The total profit was 180000.

Formula:
Ratio of Profit = ratios of product of Amount invested and time

Calculation:
Let the investments by A , B and C be 4x, 6x and 9x respectively
Ratio of profit = amount × time
Ratio of profits of A, B and C = 4x × 3 : 6x × 1 : 9x × 4 = 2x : x : 6x
Profit of B = x/9x × profit = 1/9 × 180000 = 20000

Given:
P, Q and R invest in ratio  6 : 6 : 8 in 1 year and 20% donate in school 
And R profit greater than  Q in Rs. 600

Calculation: 
Let total profit = 100 unit 
20% donates in school 
⇒ 100 unit × 20% = 20 unit 
 Remaining = 80 unit
 According to question,
total profit = P + Q + R = 6 + 8 + 6 = 20x
⇒ 20x = 80 unit 
⇒ 1x = 4 unit 
So, profit of P's = 6 × 4 = 24,  R's = 8 × 4 = 32 
And Q's = 6 × 4 = 24 
We have given,
Profit of R is Rs.600 greater than Profit of Q
⇒  32 - 24 = 600
⇒ 8 = 600
⇒ Total profit = 600/8 x 100 = 7500
Total profit  Rs. 7500

Given:
Amount invested by A = Rs 12000
Amount invested by B = Rs 16000
Amount invested by C = Rs 15000
Total profit after 2 years = Rs. 45600

To find:
The share of C in a profit

Concept used:
Total amount = amount invested × number of months

Calculation:
Total amount invested by A = 12000 × 24
⇒ Total amount invested by A = 288000
⇒ Total amount invested by B = 16000 × 24
⇒ Total amount invested by B = 384000
⇒ Total amount invested by C = 15000 × 16
⇒ Total amount invested by C = 240000
⇒ The ratio of their investment ie. A : B : C = 288000 : 384000 : 240000
⇒ The ratio of their investment ie. A : B : C = 6 : 8 : 5
⇒ C's share in profit = (5/19) × 45600
⇒ C's share in profit = 12000
∴ The C's share in profit is Rs. 12000.

Given:
A’s contribution = Rs. 4500
Profit ratio = 3 : 4

Formula used:

Calculation:
Let the Contribution of B is Rs. x
A invested for 12 months and B invested for (12 – 4) = 8 months
⇒ (4500 × 12)/(x × 8) = ¾
⇒ (4500 × 12 × 4)/(3 × 8) = x
⇒ x = 9000
∴ Contribution of B to the business is 9000.

In the 1st year,
Let, investment of A = Rs. 4x
Investment of B = Rs. 7x
Investment of C = Rs. 8x
In the 2nd year,
Investment of A = Rs. (4x + 4x × 50/100) = Rs. 6x
Investment of B = Rs. 7x
Investment of C = Rs. (8x/2) = Rs. 4x
∴ Weighted ratio of investment of A, B and C,
⇒ (4x × 12 + 6x × 12) ∶ (7x × 24) ∶ (8x × 12 + 4x × 12)
⇒ 120x ∶ 168x ∶ 144x
⇒ 5 ∶ 7 ∶ 6
Total profit = Rs. 14400
∴ Share of B = 14400 × (7/18) = Rs. 5600