How to solve partnership problems questions - Part 2

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How to solve partnership problems questions?

Introduction

On the Nithra Jobs site, we have given a list of solved problems on the topic of Partnership. If you are interested in learning these given sums visit our site. Improve your knowledge in business by solving business partnership questions regularly. It is also useful for job seekers to clear up the upcoming competitive exams. To know about the partnership problems formula visit this link.

6. M, N, O subscribe Rs. 5000 for a business. M subscribes Rs. 400 more than N and N subscribes Rs. 500 more than O. Out of a total profit of Rs. 3500, M receives:

Answer: Rs.1470

Explanation:

Let O = x, N = x + 500; M = x + 500 + 400

So the total amount = M + N + O

(x) + ( x + 500 ) + ( x + 500 + 400 ) = Rs. 5000

3x + 1400 = 5000

3x = 5000-1400

3x = 3600

x = 3600 / 3

x = 1200

∴ O = Rs. 1200

Then N = x + 500

= 1200 + 500

= Rs. 1700

M = x + 500 + 400

= 1200 + 900

= Rs. 2100

Ratio of their investement

M : N : O = 2100 : 1700 : 1200 = 21 : 17 : 12

∴ M's share = 3500 * [ 21 / ( 21 + 17 + 12 ) ]

= 3500 * ( 21 / 50 )

= Rs.1470

M's share = Rs.1470

7. X and Y started a partnership business investing some amount in the ratio of 7 : 4. Z joined then after six months with an amount equal to that of X. In what proportion should the profit at the end of one year be distributed among X, Y and Z?

Answer: 14 : 8 : 7

Explanation:

Let the initial investments of X and Y be 7x and 4x

Ratio of their investment

X : Y : Z = (7x * 12) : (4x * 12) : (7x * 6)

= ( 7 * 12 ) : ( 4 * 12 ) : ( 7 * 6 )

= 84 : 48 : 42

= 42 : 24 : 21

= 14 : 8 : 7

Ratio of their investment = 14 : 8 : 7

8. Suresh, karthi and Anu invested Rs. 4500, Rs. 2500 and Rs. 4500 respectively in a business. Suresh and Karthi left after six months. If after eight months, there was a gain of Rs. 4160, then what will be the share of karthi?

Answer: Rs. 800

Explanation:

Ratio of their investment

Suresh : karthi : Anu = ( 4500 * 6 ) : ( 2500 * 6 ) : ( 4500 * 8 )

= ( 45 * 6 ) : ( 25 * 6 ) : ( 45 * 8 )

= ( 9 * 6 ) : ( 5 * 6 ) : ( 9 * 8 )

= 54 : 30 : 72

= 27 : 15 : 36

= 9 : 5 : 12

karthi's share = 4160 * [ 5 / ( 9 + 5 + 12 ) ]

= 4160 * ( 5 / 26 )

= 160 * 5

= Rs. 800

Karthi's share = Rs. 800

9. A and B invest in a business in the ratio 3 : 2. If 5% of the total profit goes to charity and A's share is Rs. 855, the total profit is:

Answer: Rs. 1500

Explanation:

Let's assume that the total profit made by the business is P.

As per the given ratio, A's share of the profit will be 3x

B's share will be 2x, where x is a common ratio.

It is given that A's share of the profit is Rs. 855, so we can write:

3x = 855

x = 855/3

x = 285

∴ A's share of the profit is 3x = 3 * 285

= Rs. 855

B's share of the profit is 2x = 2 * 285

= Rs. 570.

We know that 5% of the total profit goes to charity, so the remaining 95% is divided between A and B in the ratio 3 : 2.

The total profit can be written as:

Total Profit = (A's share + B's share) / 0.95

= (855 + 570) / 0.95

= 1425 / 0.95

= Rs. 1500

The total profit made by the business is Rs. 1500.

10. Revathi, Usha and Roshini entered into a partnership by investing Rs. 20000, Rs X, and Rs. 22000 respectively for 6 months, 8 months and 10 months respectively. If Usha earns a profit of Rs. 16500 out of a total profit of Rs. 44550, find the total investment done by all three.

Answer: Rs. 67000

Explanation:

Revathi : Usha : Roshini = ( 20000 * 6 ) : ( x * 8 ) : ( 22000 * 10 )

= ( 20000 * 3 ) : ( x * 4 ) : ( 22000 * 5 )

= ( 10000 * 3 ) : ( x * 2 ) : ( 11000 * 5 )

= 30000 : 2x : 55000

= 15000 : x : 27500

Usha's share = 44550 * [ x / ( 15000 + x + 27500 ) ]

16500 = 44550 * [ x / ( 42500 + x ) ]

16500 * ( 42500 + x ) = 44550x

701250000 + 16500x = 44550x

701250000 = 44550x - 16500x

701250000 = 28050x

x = 701250000 / 28050

= 70125000 / 2805

= 25000

So total investment = 20000 + 25000 + 22000

= Rs. 67000

Total investment = Rs. 67000

Practice Questions:

1. Karthi started a business with Rs.12500 and after 4 months, Kavin joined him with Rs.30000. Karthi received Rs.29000 including 10% of profit as commission for managing the business. What amount did Kavin receive?

2. A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Rs. 6500 for 6 months, B, Rs. 8400 for 5 months and C, Rs. 10,000 for 3 months. A want to be the working member for which, he was to receive 5% of the profits. The profit earned was Rs. 7400. Calculate the share of B in the profit.

3. A, B and C enter into a partnership in the ratio 7/2 :4/3 :6/5. After 4 months, A increases his share 50%. If the total profit at the end of one year be Rs. 21,600, then B's share in the profit is?

4. 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:

5. Three partners shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 8 months and 7 months respectively. What was the ratio of their investments?

Conclusion

Partnership sums are an important part of business and finance that require a strong understanding of basic mathematical concepts. By working through these partnership problems with solutions, individuals can learn how to calculate profits and losses and develop their analytical and problem-solving skills.