• When two or more than two persons run a business jointly, they are called partners and the deal is known as partnership.
2. Ratio of Divisions of Gains
I. When investments of all the partners are for the same time, the gain or loss is distributed among the partners in the ratio of their investments.
Suppose A and B invest Rs. x and Rs. y respectively for a year in a business, then at the end of the year:
(A's share of profit) : (B's share of profit) = x : y.
II. When investments are for different time periods, then equivalent capitals are calculated for a unit of time by taking (capital x number of units of time). Now gain or loss is divided in the ratio of these capitals.
Suppose A invests Rs. x for p months and B invests Rs. y for q months then,
(A's share of profit) : (B's share of profit)= xp : yq.
3. Working and Sleeping Partners
• A partner who manages the business is known as a working partner and the one who simply invests the money is a sleeping partner.
1. Chakri and Rahul started a business investing amounts of Rs.2,50,000 and Rs.4,00,000 respectively. If Rahul's share in the profit earned by them is Rs.16,000, what is the total profit earned by them together? (In Rs.)
A) 30,000 B) 14,000 C) 15,000
D) 20,000 E) 26,000
2. Akhtar starts business with Rs.15,000 and Sanjay joins him after 6 months with an investment of Rs.40,000. What will be the ratio of the profits A and B at the end of year?
A) 10 : 13 B) 11 : 12 C) 5 : 6
D) 3 : 4 E) 7 : 8
3. Ravi, Sharath and Krishna together start a business in partnership. The ratio of their capitals is 4 : 7 : 9. If their annual profit is Rs.60,000, what will be Krishna's share (in Rs.) in this profit?
A) 24,000 B) 25,000 C) 36,000
D) 20,000 E) 27,000
4. Akhil , Samdish and Varun start a business by investing Rs.9000, Rs.12,000 and Rs.21,000 respectively. At the end of year, they got a profit of Rs.2800. What is the share of Varun in profit? (In Rs.)
A) 1400 B) 1500 C) 1600
D) 1100 E) 1200
5. Ajay and Bheem invest in the ratio of 2 : 5 respectively. After 3 months , Charan enters the business with the investment of the capital equal to that of Bheem. What will be the ratio of the profits of Ajay, Bheem and Charan at the end of year?
A) 9 : 16 : 25 B) 12 : 14 : 17
C) 8 : 20 : 15 D) 9 : 13 : 15 E) 11 : 20 : 12
6. Harsha and Kiran started a business initially with Rs.19,500 and Rs.26,000, respectively. Investments done by both the persons are in for different time periods. If the total profit is Rs.2400, what is the profit of Harsha?
A) Rs.1100 B) Rs.1200 C) Rs.1300
D) Rs.1400 E) Data inadequate
7. Sachin, Sehwag and Yuvraj together start a business, Sehwag invests 1/6 of the total capital while investments of Sachin and Yuvraj are equal. If the annual profit of this investment is Rs.48,000, find the difference between the profits of Sehwag and Yuvraj.
A) Rs.9000 B) Rs.11,000 C) Rs.12,000
D) Rs.15,000 E) Rs.16,000
8. Vikram and Mohanlal started a business by investing Rs.20,000 and Rs.25,000, respectively. After 4 months Mohanlal left and Sachin joined by investing Rs.15,000. At the end of the year, there was a profit of Rs.23,000, what is Sachin's share?
A) Rs.18,000 B) Rs.24,000 C) Rs.12,000
D) Rs.16,000 E) Rs.30,000
9. Harshad, Sucheta and RamGopal entered into partnership in a business. Harshad got 60% of profit. Sucheta and RamGopal distributed the remaining profit equally. If RamGopal got Rs.800 less than Harshad, the total profit (in Rs.) was ....
A) 1500 B) 1000 C) 2000
D) 4000 E) 5000
10. Vijay and Kumar started business by investing Rs.20,000 and Rs.25,000 respectively. After 5 months Kumar left the business and Sushmitha joined the business with the sum of Rs.30,000. The profit earned at the end of year is Rs.47,000. What is the share of Kumar in profit (approximately)? (In Rs.)
A) Rs.10,000 B) Rs.12,050 C) Rs.10,215
D) Rs.10,500 E) Rs.10,550
11. Ajay started a business. After 4 months from the start of the business, Bharat and Charan joined. The respective ratio between the investments of Ajay, Bharat and Charan was 4 : 6 : 5. If Ajay's share in annual profit was Rs.1200 more than Charan's share. What was the total annual profit earned?
A) Rs.20,400 B) Rs.23,400 C) Rs.13,500
D) Rs.61,400 E) None of these
12. Ankit and Bheem started a business with investments of Rs.3500 and Rs.2500 respectively. After 4 months Charles joined with Rs.6000. If the difference between Charle's share and Bheem's share in the annual profit was Rs.3000. What was the total annual profit? (In Rs.)
A) 25000 B) 22000 C) 14000
D) 15000 E) 20000
13. Santosh has divided his total money in his will in such a way that half of it goes to his wife, 2/3 rd of the remaining among his three sons equally and the rest among his four daughters equally. If each daughter gets Rs.15,245. How much money will each son get?
A) Rs.36,693.3333 B) Rs.39,513.3333
C) Rs.40,653.3333 D) Rs.54,126.3333
14. Sunetra invested an amount of Rs.50,000 to start a software business. After six months Nikhil joined her with an amount of Rs.80,000. At the end of 3 years they earned a profit of Rs.11,165. What is Sunetra's share in the profit?
A) Rs.2795 B) Rs.6785 C) Rs.4765
D) Rs.4785 E) Rs.5785
1-E 2-D 3-E 4-A 5-C 6-E 7-C 8-A 9-C 10-C 11-A 12-E 13-C 14-D
1. As we know ratio of profits = Ratio of
Chakri's share = Rahul's share
= 250000 : 400000 = 5 : 8
Let Chakri's share = 5x, Rahul's share = 8x
According to the question 8x = 16000
Total profit = 5x + 8x
= 13x = 13 × 2000 = Rs.26,000
2. A's share : B's share
= (15000 × 12) : 40000 × (12 − 6)
= 30 : 40 = 3 : 4
3. Let Ravi's share = 4x, Sharath's share = 7x
Krishna's share = 9x
According to the question,
Krishna's share = 9x = 9 × 3000 = Rs.27,000
4. Share of Akhil : Share of Samdish :
Share of Varun
= 9000 : 12000 : 21000 = 3 : 4 : 7
Total earned profit = Rs.2800
Share of Varun in profit = × 2800 = 1400
5. Let investment of Ajay = 2x
Investment of Bheem = 5x
Investment of Charan = 5x
As we know ratio of profits = Ratio of investments
A's share : B's share : C's share
= 2x × 12 : 5x × 12 : 5x × (12 − 3)
= 24x : 60x : 45x
= 8 : 20 : 15
6. Time is not given in the question. So, we cannot
find the profit of Harsha. Hence, the data
7. Investment of Sehwag = of total capital
Investments of Sachin and Yuvraj each = of total capital
Now, Sachin's share : Sehwag's share :
Let Sachin's share = 5x
Sehwag's share = 2x, Yuvraj's share = 5x
According to the question,
5x + 2x + 5x = 48000
Difference in profit of Sehwag and Yuvraj
= 5x − 2x = 3x = 3 × 4000 = Rs.12,000
8. Vikram's share : Mohanlal's share :
= (20000 × 12) : (25000 × 4) : (15000 × 8)
= 240000 : 100000 : 120000
= 24 : 10 : 12 = 12 : 5 : 6
Let Vikram's share = 12x
Mohanlal's share = 5x, Sachin's share = 6x
According to the question,
Sachin's share = 6x = 6 × 3000 = Rs.18,000
9. Let the total profit be Rs.100%
Then, Harshad's share in profit = 60%
Remaining profit = 40%
Sucheta's share in profit = 20%
RamGopal's share in profit = 20%
According to the question, 40% = 800
Total profit = 100% = Rs.2000
10. Ratio of equivalent capitals of Vijay, Kumar
= (20000 × 12) : (25000 × 5) : (30000 × 7)
= 48 : 25 : 42
Let Vijay's share = 48x,
Kumar's share = 25x
Sushmitha's share = 42x
According to the question,
Kumar's share = 25x = 25 × 408.6
11. Ratio of the equivalent capitals of Ajay,
Bharat and Charan for 1 month
= (12 × 4) : (6 × 8) : (5 × 8)
= 48 : 48 : 40 = 6 : 6 : 5
Sum of ratios = 6 + 6 + 5 = 17 (parts)
If total annual profit be Rs.a then
Ajay's share − Charan's share = 1200
12. Ratio of equivalent capitals of A, B and C for
= (3500 × 12) : (2500 × 12) : (6000 × 8)
= (35 × 12) : (25 × 12) : (60 × 8) = 7 : 5 : 8
Sum of the terms of the ratio = 7 + 5 + 8 = 20
According to the question, If the total annual
profit be Rs.x, then difference of shares of C
and B = Rs.3000
13. Let the total money be x
Half of the total money goes to wife =
of the is divided equally among three sons.
The share of each son =
and, is divided equally among four daughters.
The share of each daughter =
14. The ratio of capital invested by each partner
i.e. Sunetra and Nikhil for 1 month in order
to get the same profit is:
36 × 50000 : 30 × 80000 = 3 : 4
Share of Sunetra out of Rs.11165