Quantitative Techniques · Micro-test
Partnership
Partners share profit in the ratio of what each put in, multiplied by how long it stayed in. Every partnership question is that ratio, set up correctly and then applied to the profit.
10 questions · 5 minutes · instant scoring
What this topic actually tests
Each partner's share of profit is proportional to capital × time. If A puts in Rs 30,000 for 12 months and B puts in Rs 40,000 for 8 months, their ratio is 30,000 × 12 : 40,000 × 8 = 3,60,000 : 3,20,000 = 9 : 8. To divide a profit P in the ratio a : b, A gets P × a ÷ (a + b). When capital changes during the year, add up capital × months for each period: Rs 50,000 for six months and then Rs 30,000 for six months counts as 3,00,000 + 1,80,000 = 4,80,000. When the capitals are given as fractions, bring them to a common denominator first: 1/2 : 1/3 : 1/4 becomes 6 : 4 : 3. A working partner's salary or commission comes off the profit before the rest is shared. Worked example: a Rs 50,000 profit, with 10% paid to the working partner first, leaves Rs 45,000 to be shared in the capital ratio.
The common trap on this topic
The common error is to share profit in the ratio of capital alone when the partners were in for different lengths of time. A partner who joins after four months has money working for eight, not twelve. The second error is sharing the whole profit when a salary or commission is due to a working partner: pay that first and share the remainder.
Take the micro-test
A invests Rs 20,000 and B invests Rs 30,000 in a business for one year. The profit is Rs 15,000. What is A's share?
A invests Rs 40,000 for 12 months and B invests Rs 60,000 for 6 months. Out of a profit of Rs 21,000, what is B's share?
A, B and C invest in the ratio 2 : 3 : 5 for the same period. The profit is Rs 50,000. What is C's share?
A starts a business with Rs 30,000. After 4 months B joins with Rs 40,000. At the end of the year the profit is Rs 34,000. What is A's share?
A and B share profit in the ratio 5 : 4. A's capital was invested for 10 months and B's for 8 months. What was the ratio of their capitals?
A invests Rs 50,000 and withdraws Rs 20,000 after 6 months. B invests Rs 40,000 for the whole year. The year's profit is Rs 30,000. What is A's share?
A invests Rs 60,000 as a sleeping partner and B invests Rs 40,000 and runs the business. B first receives 10% of the profit for running it, and the rest is shared in the ratio of capital. The profit is Rs 50,000. How much does B receive in all?
The capitals of A and B are in the ratio 3 : 5 and the periods of their investment are in the ratio 4 : 3. In what ratio do they share profit?
A, B and C invest capitals in the ratio 1/2 : 1/3 : 1/4 for the same period. The profit is Rs 39,000. What is B's share?
A and B invest for the same period. Out of a profit of Rs 12,000, A receives Rs 4,800. A invested Rs 24,000. How much did B invest?
Partnership: answers and explanations
A invests Rs 20,000 and B invests Rs 30,000 in a business for one year. The profit is Rs 15,000. What is A's share?
Answer: B. Rs 6,000
The ratio is 20,000 : 30,000 = 2 : 3. A gets 15,000 × 2 ÷ 5 = Rs 6,000.
A invests Rs 40,000 for 12 months and B invests Rs 60,000 for 6 months. Out of a profit of Rs 21,000, what is B's share?
Answer: B. Rs 9,000
A : B = 40,000 × 12 : 60,000 × 6 = 4,80,000 : 3,60,000 = 4 : 3. B gets 21,000 × 3 ÷ 7 = Rs 9,000.
A, B and C invest in the ratio 2 : 3 : 5 for the same period. The profit is Rs 50,000. What is C's share?
Answer: B. Rs 25,000
C's part is 5 of 2 + 3 + 5 = 10 parts: 50,000 × 5 ÷ 10 = Rs 25,000.
A starts a business with Rs 30,000. After 4 months B joins with Rs 40,000. At the end of the year the profit is Rs 34,000. What is A's share?
Answer: B. Rs 18,000
A : B = 30,000 × 12 : 40,000 × 8 = 3,60,000 : 3,20,000 = 9 : 8. A gets 34,000 × 9 ÷ 17 = Rs 18,000.
A and B share profit in the ratio 5 : 4. A's capital was invested for 10 months and B's for 8 months. What was the ratio of their capitals?
Answer: D. 1 : 1
Capital × time is in the ratio 5 : 4, so capital is in the ratio 5/10 : 4/8 = 1/2 : 1/2 = 1 : 1.
A invests Rs 50,000 and withdraws Rs 20,000 after 6 months. B invests Rs 40,000 for the whole year. The year's profit is Rs 30,000. What is A's share?
Answer: A. Rs 15,000
A: 50,000 × 6 + 30,000 × 6 = 4,80,000. B: 40,000 × 12 = 4,80,000. The ratio is 1 : 1, so A gets Rs 15,000.
A invests Rs 60,000 as a sleeping partner and B invests Rs 40,000 and runs the business. B first receives 10% of the profit for running it, and the rest is shared in the ratio of capital. The profit is Rs 50,000. How much does B receive in all?
Answer: A. Rs 23,000
B's 10% is Rs 5,000, leaving Rs 45,000 shared 60,000 : 40,000 = 3 : 2. B's part is 45,000 × 2 ÷ 5 = Rs 18,000, so B receives 5,000 + 18,000 = Rs 23,000.
The capitals of A and B are in the ratio 3 : 5 and the periods of their investment are in the ratio 4 : 3. In what ratio do they share profit?
Answer: D. 4 : 5
Profit ratio = 3 × 4 : 5 × 3 = 12 : 15 = 4 : 5.
A, B and C invest capitals in the ratio 1/2 : 1/3 : 1/4 for the same period. The profit is Rs 39,000. What is B's share?
Answer: D. Rs 12,000
Over the common denominator 12, the ratio is 6 : 4 : 3, which is 13 parts. B gets 39,000 × 4 ÷ 13 = Rs 12,000.
A and B invest for the same period. Out of a profit of Rs 12,000, A receives Rs 4,800. A invested Rs 24,000. How much did B invest?
Answer: C. Rs 36,000
B receives 12,000 − 4,800 = Rs 7,200. Capitals are in the ratio of shares, so B invested 24,000 × 7,200 ÷ 4,800 = Rs 36,000.
FAQ
How is profit shared in a partnership?
In the ratio of each partner's capital multiplied by the time it was invested, unless the partners have agreed otherwise.
What if a partner joins late?
Multiply that partner's capital by the months it was actually invested. A partner joining after 4 months of a 12-month year counts 8 months.
How is a working partner's salary handled?
Deduct it from the profit first, give it to the working partner, and share the remainder in the capital ratio.
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