Aptitude-Partnership problems

(6) A, B, and C start a business together. A invests Rs. 10,000 for the whole year, B invests Rs. 8,000 for 9 months, and C invests Rs. 12,000 for 8 months. If the profit at the end of the year is Rs. 9,180, find C’s share.

• (a) Rs. 3,680
• (b) Rs. 3,000
• (c) Rs. 2,500
• (d) Rs. 4,000

Answer

Correct Answer: (a) Rs. 3,680
Ratio of their investments = (10000 x 12) : (8000 x 9) : (12000 x 8)
= 120000 : 72000 : 96000
= 5 : 3 : 4
C’s share = Rs. 9,180 x (4/12) = Rs. 3,680.

(7) M and N start a business with investments in the ratio 7:6. After 8 months, M withdraws his investment. If the total annual profit is Rs. 8,400, find N’s share.

• (a) Rs. 3,600
• (b) Rs. 4,800
• (c) Rs. 4,200
• (d) Rs. 5,000

Answer

Correct Answer: (b) Rs. 4,800
M’s investment period = 7 x 8 months.
N’s investment period = 6 x 12 months.
Ratio of their investment periods = 56 : 72
= 7 : 9
N’s share = Rs. 8,400 x (9/16) = Rs. 4,800.

(8) In a business, S invests Rs. 20,000 for 6 months, T invests Rs. 15,000 for 8 months, and U invests Rs. 25,000 for 4 months. Find the ratio of their profits at the end of the year.

• (a) 4:3:5
• (b) 5:4:5
• (c) 6:5:4
• (d) 3:4:5

Answer

Correct Answer: (b) 5:4:5
Ratio of their investments = (20000 x 6) : (15000 x 8) : (25000 x 4)
= 120000 : 120000 : 100000
= 5 : 4 : 5.

(9) Three friends A, B, and C start a business. A invests twice as much as B, and B invests thrice as much as C. If C invests Rs. 5,000, and the total profit is Rs. 8,000, find A’s share.

• (a) Rs. 4,800
• (b) Rs. 4,000
• (c) Rs. 3,200
• (d) Rs. 3,600

Answer

Correct Answer: (b) Rs. 4,000
C’s investment = Rs. 5,000.
B’s investment = 3 x Rs. 5,000 = Rs. 15,000.
A’s investment = 2 x Rs. 15,000 = Rs. 30,000.
Ratio of their investments = 30,000 : 15,000 : 5,000
= 6 : 3 : 1
A’s share = Rs. 8,000 x (6/10) = Rs. 4,800.

(10) P, Q, and R start a business. P invests 1/3 of the total capital, Q invests 1/4 of the total capital, and the rest is invested by R. If the annual profit is Rs. 12,000, calculate R’s share.

• (a) Rs. 6,000
• (b) Rs. 5,000
• (c) Rs. 4,000
• (d) Rs. 7,000

Answer

Correct Answer: (a) Rs. 6,000
P’s share = 1/3, Q’s share = 1/4.
R’s share = 1 – (1/3 + 1/4) = 5/12.
R’s share of the profit = Rs. 12,000 x (5/12) = Rs. 6,000.

(11) In a business, A invests Rs. 4000 for the whole year, B invests Rs. 6000 for 9 months, and C invests Rs. 8000 for 6 months. If the total profit at the end of the year is Rs. 6200, what is B’s share in the profit?

• (a) Rs. 2400
• (b) Rs. 1800
• (c) Rs. 2000
• (d) Rs. 2200

Answer

Correct Answer: (c) Rs. 2000
Ratio\ of\ their\ investments = (4000 \times 12) : (6000 \times 9) : (8000 \times 6)
= 48000 : 54000 : 48000
= 5 : 6 : 5
B's\ share = Rs.\ 6200 \times \frac{6}{16} = Rs.\ 2000.

(12) Three partners A, B, and C start a business. A’s investment is thrice that of B and B’s investment is twice that of C. If C invested Rs. 2000, and the total profit is Rs. 6000, find A’s share of the profit.

• (a) Rs. 3600
• (b) Rs. 2400
• (c) Rs. 3000
• (d) Rs. 2000

Answer

Correct Answer: (a) Rs. 3600
Let\ C's\ investment = x,\ then\ B's\ investment = 2x\ and\ A's\ investment = 6x.
C's\ investment = Rs.\ 2000,\ so\ A's\ investment = 6 \times 2000 = Rs.\ 12000.
Ratio\ of\ their\ investments = 12000 : 4000 : 2000<br /> = 6 : 2 : 1
A's\ share = Rs.\ 6000 \times \frac{6}{9} = Rs.\ 3600.

(13) M, N, and O started a business. M invested Rs. 3500, N invested Rs. 4500, and O joined them after 3 months with an investment of Rs. 5000. If the profit at the end of the year is Rs. 5400, calculate O’s share of the profit.

• (a) Rs. 2000
• (b) Rs. 1500
• (c) Rs. 1800
• (d) Rs. 1600

Answer

Correct Answer: (b) Rs. 1500
Ratio\ of\ their\ investments = (3500 \times 12) : (4500 \times 12) : (5000 \times 9)
= 42000 : 54000 : 45000
= 7 : 9 : 7.5
O's\ share = Rs.\ 5400 \times \frac{7.5}{23.5} \approx Rs.\ 1500.

(14) Partners A, B, and C start a business. A invests Rs. 10000 for 6 months, B invests Rs. 8000 for 8 months, and C invests Rs. 6000 for the entire year. If the profit at the end of the year is Rs. 9000, find the share of C in the profit.

• (a) Rs. 3000
• (b) Rs. 2400
• (c) Rs. 3600
• (d) Rs. 2700

Answer

Correct Answer: (b) Rs. 2400
Ratio\ of\ their\ investments = (10000 \times 6) : (8000 \times 8) : (6000 \times 12)
= 60000 : 64000 : 72000
= 5 : 5.33 : 6
C's\ share = Rs.\ 9000 \times \frac{6}{16.33} \approx Rs.\ 2400.

(15) D, E, and F entered into a partnership by investing in the ratio of 2:3:4. After 6 months, D withdrew half of his investment, and after 8 months, F invested Rs. 2000 more. If the total annual profit is Rs. 8400, what is E’s share?

• (a) Rs. 3000
• (b) Rs. 3600
• (c) Rs. 2800
• (d) Rs. 2400

Answer

Correct Answer: (b) Rs. 3600
Let\ the\ common\ multiple\ of\ investments\ be\ x.\ D's\ investment = 2x,\ E's = 3x,\ F's = 4x.
D's\ effective\ investment = 2x \times 6 + x \times 6,\ E's = 3x \times 12,\ F's = 4x \times 8 + 6x \times 4.
Ratio\ = 12x : 36x : 44x = 1 : 3 : 3.67.
E's\ share = Rs.\ 8400 \times \frac{3}{7.67} \approx Rs.\ 3600.