Practice Partnership questions covering profit-sharing ratios, capital invested for varying time periods, simple and compound partnerships, and working vs. sleeping partners for Quantitative Aptitude.
Question 2
Four friends (A, B, C and D) started a business in partnership by investing capitals in the proportion 3 : 5 : 4 : 6. During the period of one-year, these capitals were utilized in the proportion of 6 : 4 : 5 : 3 respectively. If, at the end of the year, a profit of Rs. 15,550 was made, what will be the share of D?
Explanation
Capital x time for each: A = 3 × 6 = 18, B = 5 × 4 = 20, C = 4 × 5 = 20, D = 6 × 3 = 18.
The ratio is 18 : 20 : 20 : 18 and the total is 76.
D's share = 1876 × 15550 = Rs. 3682.89.
The ratio is 18 : 20 : 20 : 18 and the total is 76.
D's share = 1876 × 15550 = Rs. 3682.89.
Question 3
Three friends (Amar, Mohan and Sham) started partnership business by investing Rs. 1,00,000, Rs. 1,40,000 and Rs. 1,60,000 respectively. After eight months, Ramesh joins them with his capital of Rs. 50,000. If, at the end of the year, a profit of Rs. 30,500 was made, what would be the difference between the shares of Sham and Mohan?
Explanation
Capital x time: Amar = 1,00,000 × 12, Mohan = 1,40,000 × 12, Sham = 1,60,000 × 12 and Ramesh = 50,000 × 4.
The ratio = 1200 : 1680 : 1920 : 200 = 30 : 42 : 48 : 5, and the total = 125.
1 part = 30500125 = Rs. 244. Sham - Mohan = (48 - 42) × 244 = Rs. 1464.
The ratio = 1200 : 1680 : 1920 : 200 = 30 : 42 : 48 : 5, and the total = 125.
1 part = 30500125 = Rs. 244. Sham - Mohan = (48 - 42) × 244 = Rs. 1464.
Question 4
In a partnership for a business, Jay invests Rs.6000 for complete year & Viru invests Rs.3000 for 6 months. What is Viru’s share if they earn Rs.240 as profit?
Explanation
The profit is shared in the ratio of investment × time.
Jay : Viru = (6000 × 12) : (3000 × 6) = 72,000 : 18,000 = 4 : 1.
Viru's share = 15 × 240 = Rs. 48.
Jay : Viru = (6000 × 12) : (3000 × 6) = 72,000 : 18,000 = 4 : 1.
Viru's share = 15 × 240 = Rs. 48.
Question 5
Ravi started off with a business with a capital of Rs.60000. Later he was joined by Kishan with Rs.40000 as his share. If Kishan received 13rd of the total profit after 1 year, for how many months did he invest?
Explanation
Kishan received 13 of the profit, so Ravi received 23, and the ratio = 1 : 2.
Ravi's investment = 60,000 × 12 = 720,000 and Kishan's = 40,000 × t.
40000t720000 = 12, so t = 9 months.
Ravi's investment = 60,000 × 12 = 720,000 and Kishan's = 40,000 × t.
40000t720000 = 12, so t = 9 months.
Question 6
Akash and Akshay are business partners. Akash invests Rs 35,000 for a period of 8 months and Akshay invests Rs 42,000 for a period of 10 months. Out of a total profit of Rs 31,570 what is Akash’s share?
Explanation
The profit is shared in the ratio of investment × time.
Akash : Akshay = (35,000 × 8) : (42,000 × 10) = 280,000 : 420,000 = 2 : 3.
Akash's share = 25 × 31,570 = Rs. 12,628.
Akash : Akshay = (35,000 × 8) : (42,000 × 10) = 280,000 : 420,000 = 2 : 3.
Akash's share = 25 × 31,570 = Rs. 12,628.
Question 7
P gave Rs. 12000 for starting a business. Q gave Rs. 16000. What will be share of profit of R after 2 years, if R comes after 8 months with his Rs. 15000 and profit earned by P, Q and R is Rs. 45600?
Explanation
P invests Rs. 12,000 for 24 months, Q invests Rs. 16,000 for 24 months and R invests Rs. 15,000 for 16 months.
P : Q : R = 288000 : 384000 : 240000 = 6 : 8 : 5.
R's share = 519 × 45600 = Rs. 12,000.
P : Q : R = 288000 : 384000 : 240000 = 6 : 8 : 5.
R's share = 519 × 45600 = Rs. 12,000.
Question 8
Rs. 15000 were invested by Ram and Shyam together to start a small business. They got a profit of Rs. 2000 at the end of the year. Shyam took his profit share of Rs. 600. How much did Ram invest?
Explanation
Shyam's profit share = 6002000 = 30%, so Shyam's investment = 30% of 15000 = Rs. 4500 (both invested for the same time).
Ram's investment = 15000 - 4500 = Rs. 10,500.
Ram's investment = 15000 - 4500 = Rs. 10,500.
Question 9
A small library is started by Prakash and John. Prakash invests Rs. 2000 and John Rs. 5000 for 9 and 7 months respectively. In what ratio will John and Prakash share the profit of Rs. 1100?
Explanation
Prakash : John = (2000 × 9) : (5000 × 7) = 18000 : 35000 = 18 : 35.
John : Prakash = 35 : 18.
John : Prakash = 35 : 18.
Question 10
P and Q start a cafe with a capital Rs. 20,000 and Rs. 40,000 respectively. After a year, out of the profit of Rs. 15000, P gets his share of profit plus some money as his salary. In total if P gets Rs. 7000, what is the salary amount he received?
Explanation
The capitals are in the ratio 20,000 : 40,000 = 1 : 2, so P's share of the profit = 13 × 15000 = Rs. 5000.
P gets Rs. 7000 in total, so the salary = 7000 - 5000 = Rs. 2000.
P gets Rs. 7000 in total, so the salary = 7000 - 5000 = Rs. 2000.
Question 11
Ramesh and Suresh start a hotel. Ramesh invested Rs. 6000 and Suresh invested Rs. 5000. Ramesh’s investment was for 4 months and Suresh’s was for 8 months. If total profit was Rs. 6000, how much more profit than Ramesh did Suresh get?
Explanation
Ramesh : Suresh = (6000 × 4) : (5000 × 8) = 24000 : 40000 = 3 : 5.
Ramesh gets 38 × 6000 = Rs. 2250 and Suresh gets Rs. 3750.
The difference = 3750 - 2250 = Rs. 1500.
Ramesh gets 38 × 6000 = Rs. 2250 and Suresh gets Rs. 3750.
The difference = 3750 - 2250 = Rs. 1500.
Question 12
A started a travel agency using his Rs. 45000. B realized the profit in the business and joined after 3 months with his Rs. 60000. C came a bit late and after another 6 months invested Rs. 90000. Out of total profit of Rs. 20000 obtained after a year, what is share of C?
Explanation
A invests Rs. 45,000 for 12 months, B invests Rs. 60,000 for 9 months and C invests Rs. 90,000 for 3 months.
A : B : C = 540,000 : 540,000 : 270,000 = 2 : 2 : 1.
C's share = 15 × 20000 = Rs. 4000.
A : B : C = 540,000 : 540,000 : 270,000 = 2 : 2 : 1.
C's share = 15 × 20000 = Rs. 4000.
Question 13
A, B and C invested Rs. 10,000, Rs. 12,000 and Rs. 15,000 respectively to start a resort. P sees the growth of their business and then joins them after 8 months with Rs. 6,000. They earn a profit of Rs. 1560 at the end of the year. What would be difference of shares of profit of C and P?
Explanation
A, B and C invest for 12 months and P for 4 months (8 months after the start).
A : B : C : P = (10000 × 12) : (12000 × 12) : (15000 × 12) : (6000 × 4) = 120 : 144 : 180 : 24 = 10 : 12 : 15 : 2.
The total = 39 parts, so 1 part = 156039 = Rs. 40.
C = 600 and P = 80, so the difference = Rs. 520.
A : B : C : P = (10000 × 12) : (12000 × 12) : (15000 × 12) : (6000 × 4) = 120 : 144 : 180 : 24 = 10 : 12 : 15 : 2.
The total = 39 parts, so 1 part = 156039 = Rs. 40.
C = 600 and P = 80, so the difference = Rs. 520.
Question 14
P, Q and R start a hotel. Q and R invest equally but P invests one-fifth of the total investment amount. On getting profit of Rs. 225000, how much would be difference between profit of P and R?
Explanation
Let the total investment be T. P invests T5, and Q and R invest equally, so Q = R = 2T5.
The profit ratio P : Q : R = 1 : 2 : 2, with 5 parts. 1 part = 2250005 = Rs. 45,000.
P = Rs. 45,000 and R = Rs. 90,000, so the difference = Rs. 45,000.
The profit ratio P : Q : R = 1 : 2 : 2, with 5 parts. 1 part = 2250005 = Rs. 45,000.
P = Rs. 45,000 and R = Rs. 90,000, so the difference = Rs. 45,000.
Question 15
M invests Rs. 4000 in coaching classes. After 3 months N comes along with Rs. 8000. P comes in with Rs. 20000. The classes earn a profit of Rs. 112000 at the end of the year. If profits of M, N and Pare in ratio of 6:9:5, for how many months was P involved?
Explanation
M invests Rs. 4000 for 12 months = 48,000. N invests Rs. 8000 for 9 months = 72,000. P invests Rs. 20,000 for t months = 20,000t.
The profit ratio 6 : 9 : 5 gives M : P = 6 : 5, so 20,000t = 56 × 48,000 = 40,000.
t = 2 months.
The profit ratio 6 : 9 : 5 gives M : P = 6 : 5, so 20,000t = 56 × 48,000 = 40,000.
t = 2 months.
Question 16
Rohit starts a travel agency by investing Rs. 40000. After 4 months Raj joins the agency. Raj invests Rs.50000. What will be profit share of Raj if they earn a total of Rs. 187000 as profit in the entire year?
Explanation
Rohit invests Rs. 40,000 for 12 months = 480,000. Raj invests Rs. 50,000 for 8 months = 400,000.
The ratio = 480 : 400 = 6 : 5.
Raj's share = 511 × 187,000 = Rs. 85,000.
The ratio = 480 : 400 = 6 : 5.
Raj's share = 511 × 187,000 = Rs. 85,000.
Question 17
Ratio of profits of P, Q and R are 5 : 8 : 9 respectively. What is their investment ratio if their investment time period ratio is 2 : 5 : 8 respectively?
Explanation
The investment is proportional to profit ÷ time.
The ratio = 52 : 85 : 98. Multiply by 40: 100 : 64 : 45.
The ratio = 52 : 85 : 98. Multiply by 40: 100 : 64 : 45.
Question 18
A and B started a business in partnership. A invested Rs. 40000 for 6 months. A received Rs.6000 as his share out of the total profit of Rs. 9000, What was the amount invested by B for the whole year?
Explanation
A's share is Rs. 6000 out of Rs. 9000, so B's share = Rs. 3000 and the ratio of the profits = 2 : 1.
A invested Rs. 40,000 for 6 months = 240,000, and B invested x for 12 months = 12x.
24000012x = 2, so x = 10,000.
B invested Rs. 10,000.
A invested Rs. 40,000 for 6 months = 240,000, and B invested x for 12 months = 12x.
24000012x = 2, so x = 10,000.
B invested Rs. 10,000.
Question 19
A, B and C enter into partnership. A invests 3 times as much as B invests and B invests two third of what C invests. At the end of the year, the profit earned is Rs. 8500. What is the share of B?
Explanation
Let C invest 3x. B invests 23 of C, so B = 2x, and A invests 3 times B, so A = 6x.
A : B : C = 6x : 2x : 3x = 6 : 2 : 3.
B's share = 211 × 8500 = Rs. 1545.45.
A : B : C = 6x : 2x : 3x = 6 : 2 : 3.
B's share = 211 × 8500 = Rs. 1545.45.
Question 20
A,B and C enter into partnership. A advances Rs.1200 for 4 months, B Rs. 1400 for 8 Months and C Rs.1000 for 10 months. They gain Rs.585 altogether. Find the share of B.
Explanation
The profit is shared in the ratio of investment × time.
A : B : C = (1200 × 4) : (1400 × 8) : (1000 × 10) = 4800 : 11,200 : 10,000 = 12 : 28 : 25.
B's share = 2865 × 585 = Rs. 252.
A : B : C = (1200 × 4) : (1400 × 8) : (1000 × 10) = 4800 : 11,200 : 10,000 = 12 : 28 : 25.
B's share = 2865 × 585 = Rs. 252.
Question 21
A and B enter into a partnership with respective capitals of Rs. 20,000 and Rs. 40,000. At the end of the year, the total profit is Rs. 33,000. If A receives Rs. 15,000 as both his salary and profit, then what is his salary?
Explanation
The capitals are in the ratio 20,000 : 40,000 = 1 : 2, so A's share of the profit = 13 × 33000 = Rs. 11,000.
A receives Rs. 15,000 as salary and profit together, so his salary = 15000 - 11000 = Rs. 4000.
A receives Rs. 15,000 as salary and profit together, so his salary = 15000 - 11000 = Rs. 4000.
Question 22
P, Q, R subscribe Rs. 50,000 for a business. P subscribes Rs. 4000 more than Q and Q Rs. 5000 more than R. Out of a total profit of Rs. 25,000, what will be P's share?
Explanation
Let R subscribe x. Then Q = x + 5000 and P = x + 9000.
x + x + 5000 + x + 9000 = 50,000, so 3x = 36,000 and x = 12,000.
P = 21,000. P's share = 2100050000 × 25,000 = Rs. 10,500.
x + x + 5000 + x + 9000 = 50,000, so 3x = 36,000 and x = 12,000.
P = 21,000. P's share = 2100050000 × 25,000 = Rs. 10,500.
Question 23
A began a business with Rs. 9,000. B joined later with Rs. 10,800. After how many months did B join if the profits at the end of the year were divided in the ratio of 2: 1?
Explanation
A invested Rs. 9000 for 12 months and B invested Rs. 10,800 for (12 - m) months.
The profit ratio 2 : 1 gives 9000 × 1210800 × (12 - m) = 2, so 10800(12 - m) = 54000.
12 - m = 5, so m = 7.
B joined after 7 months.
The profit ratio 2 : 1 gives 9000 × 1210800 × (12 - m) = 2, so 10800(12 - m) = 54000.
12 - m = 5, so m = 7.
B joined after 7 months.
Question 24
A, B & C start a partnership with Rs. 2400, Rs. 3300 & Rs. 4800. A receives 18th of the profits as his salary; the rest is divided in the ratio of their capitals. At the end of the year, A's share is Rs. 390. What is the profit?
Explanation
The capitals 2400 : 3300 : 4800 are in the ratio 8 : 11 : 16, with a total of 35 parts.
Let the profit be P. A gets 18P as salary, and the remaining 78P is divided in the ratio of the capitals.
A's share = P8 + 7P8 × 835 = P8 + P5 = 13P40 = 390.
P = 390 × 4013 = 1200.
Let the profit be P. A gets 18P as salary, and the remaining 78P is divided in the ratio of the capitals.
A's share = P8 + 7P8 × 835 = P8 + P5 = 13P40 = 390.
P = 390 × 4013 = 1200.
Question 25
A and B started a business together. Their investment is in the ratio 3:2. Out of the total profit made, 5% goes to charity. A gets Rs 855 as his share. What is the total profit?
Explanation
Let total profit=P. After charity, 0.95P remains, split 3:2. A's share = 35 × 0.95P = 0.57P = 855, giving P=1500.
Question 26
X starts a business with Rs. 21000. B joins him after some months with an investment of Rs. 36000. At the end of the year, the profit is divided equally. How many months after the start of business did B join?
Explanation
For equal profit shares, investment x time must be equal: 21000 × 12 = 36000x(12-m), giving 12-m=7, so m=5.
