Partnership problems in aptitude tests deal with assessing the distribution of profits or losses among partners who invest in a business. These problems require an understanding of how investments, time periods, and other factors influence individual shares in a partnership. Such problems are common in business scenarios and help in understanding the fundamentals of joint ventures and resource pooling.

## 1. A and B start a business by investing $6000 and $8000 respectively. How should they share the profit of $4800?

a) A: $1800, B: $3000

b) A: $1920, B: $2880

c) A: $2000, B: $2800

d) A: $2200, B: $2600

### Answer:

b) A: $1920, B: $2880

### Explanation:

```
Ratio of their investments = A:B = 6000:8000 = 3:4.
Total profit = $4800.
A's share = $4800 × (3/7) = $1920, B's share = $4800 × (4/7) = $2880.
```

## 2. P, Q, and R started a business. P invested $2000, Q invested $3000, and R $5000. If the annual profit is $3600, what is R's share?

a) $1000

b) $1500

c) $2000

d) $2400

### Answer:

d) $2400

### Explanation:

```
Ratio of their investments = P:Q:R = 2000:3000:5000 = 2:3:5.
Total profit = $3600.
R's share = $3600 × (5/10) = $1800.
```

## 3. A and B started a business investing amounts in the ratio 3:2. If A's share in the profit is $3000, what is the total profit?

a) $4500

b) $5000

c) $5500

d) $6000

### Answer:

b) $5000

### Explanation:

```
Let the total profit be $x.
A's share = 3/5 of $x = $3000.
So, $x = $3000 × (5/3) = $5000.
```

## 4. Three partners A, B, and C start a business. Twice A's capital is equal to thrice B's capital and B's capital is four times C's capital. If the total profit is $4970, what is C's share?

a) $710

b) $840

c) $990

d) $1120

### Answer:

c) $990

### Explanation:

```
Let C's capital = $x, B's capital = 4x, A's capital = 6x.
Total capital = 6x + 4x + x = 11x.
C's share = $4970 × (x/11x) = $4970/11 = $450.
```

## 5. A, B, and C invest in a partnership in the ratio 7:6:8. The total profit is $2100. What is B's share?

a) $600

b) $700

c) $800

d) $900

### Answer:

a) $600

### Explanation:

```
Total ratio = 7 + 6 + 8 = 21.
B's share = $2100 × (6/21) = $600.
```

## 6. A invests $10000 for the whole year. B joins him with $20000 after 6 months. If the profit at the end of the year is $18000, what is B’s share?

a) $6000

b) $8000

c) $9000

d) $12000

### Answer:

b) $8000

### Explanation:

```
A’s investment for 12 months = $10000 × 12.
B’s investment for 6 months = $20000 × 6.
Ratio of their investments = 10000×12 : 20000×6 = 1:1.
B's share = $18000 × (1/2) = $9000.
```

## 7. P, Q, and R enter into a partnership. P contributes 1/3 of the total capital, Q 1/4th, and R the rest. If the annual profit is $4800, what is R's share?

a) $2400

b) $1800

c) $2000

d) $1600

### Answer:

a) $2400

### Explanation:

```
R's contribution = 1 - (1/3 + 1/4) = 5/12.
R's share = $4800 × (5/12) = $2000.
```

## 8. In a partnership, A invests 1/6 of the capital for 1/6 of the time, B invests 1/3 of the capital for 1/3 of the time, and C, the rest of the capital for the whole time. If the profit is $4600, find A's share.

a) $300

b) $400

c) $500

d) $600

### Answer:

a) $300

### Explanation:

```
A's share = $4600 × (1/6 × 1/6) / (1/6 × 1/6 + 1/3 × 1/3 + 1/2 × 1)
= $300.
```

## 9. X and Y start a business with investments in the ratio 5:6. After 8 months, X withdraws his capital. If the annual profit is $8400, what is X's share?

a) $3500

b) $4000

c) $4500

d) $5000

### Answer:

b) $4000

### Explanation:

```
X's time = 8 months, Y's time = 12 months.
Ratio of their investments = 5×8 : 6×12 = 2:3.
X's share = $8400 × (2/5) = $4000.
```

## 10. A, B, and C invest in a business. A invests 3 times as much as B and B invests two-thirds of what C invests. At the end of the year, the profit earned is $6600. What is A's share of the profit?

a) $2400

b) $2700

c) $3000

d) $3300

### Answer:

c) $3000

### Explanation:

```
Let C's investment = $x, B's = (2/3)x, A's = 2x.
The ratio of their investments = 2x : (2/3)x : x = 6:2:3.
A's share = $6600 × (6/11) = $3600.
```

## 11. P and Q start a business with respective investments of $6000 and $8000. If P's share in the profit is $1500, what is the total profit?

a) $2000

b) $2500

c) $3000

d) $3500

### Answer:

c) $3000

### Explanation:

```
Ratio of their investments = P:Q = 6000:8000 = 3:4.
Total profit = x.
P's share = x × (3/7) = $1500.
So, x = $1500 × (7/3) = $3500.
```

## 12. A, B, and C enter into a partnership. A contributes 1/4 of the total capital, B 1/3, and C the rest. If the annual profit is $4800, what is C's share?

a) $2000

b) $2400

c) $2800

d) $3200

### Answer:

b) $2400

### Explanation:

```
C's contribution = 1 - (1/4 + 1/3) = 5/12.
C's share = $4800 × (5/12) = $2000.
```

## 13. In a partnership, A invests 1/5 of the capital for 1/5 of the time, B invests 1/4 of the capital for 1/4 of the time, and C, the rest of the capital for the whole time. If the profit is $5500, find C's share.

a) $3000

b) $3500

c) $4000

d) $4500

### Answer:

d) $4500

### Explanation:

```
C's share = $5500 × (1 - (1/5 × 1/5 + 1/4 × 1/4)) = $4500.
```

## 14. X, Y, and Z start a business. X invests $5000 for the whole year, Y invests $6000 for 8 months, and Z $7000 for 6 months. If the annual profit is $7400, what is Y's share?

a) $2000

b) $2400

c) $2800

d) $3200

### Answer:

b) $2400

### Explanation:

```
X:Y:Z = 5000×12 : 6000×8 : 7000×6.
Calculate the ratio and find Y's share from the total profit.
```

## 15. A and B start a business together with A investing $10,000 and B $15,000. After 6 months, A withdraws half of his capital. How should they divide a profit of $4,500 at the end of the year?

a) A: $1,500, B: $3,000

b) A: $2,000, B: $2,500

c) A: $1,800, B: $2,700

d) A: $2,250, B: $2,250

### Answer:

c) A: $1,800, B: $2,700

### Explanation:

```
A's investment = $10,000 for 6 months + $5,000 for next 6 months.
B's investment = $15,000 for 12 months.
Ratio of their investments = (10000×6 + 5000×6) : 15000×12 = 90000:180000 = 1:2.
A's share = $4,500 × 1/3 = $1,500, B's share = $4,500 × 2/3 = $3,000.
```

## 16. P, Q, and R start a business. P invests $20,000, Q invests $30,000, and R invests $40,000. If the total profit at the end of the year is $8,700, what is R's share?

a) $3,000

b) $3,500

c) $4,000

d) $4,800

### Answer:

d) $4,800

### Explanation:

```
Ratio of their investments = P:Q:R = 20000:30000:40000 = 2:3:4.
Total profit = $8,700.
R's share = $8,700 × (4/9) = $3,867.
```

## 17. A starts a business with $7,000 and B joins him after a few months with $4,000. If at the end of the year, both share the profit equally, after how many months did B join?

a) 3 months

b) 5 months

c) 7 months

d) 9 months

### Answer:

b) 5 months

### Explanation:

```
Let B join after x months.
Then, 7000×12 = 4000×(12 - x)
84 = 48 - 4x
x = 9 months.
```

## 18. A, B, and C enter into a partnership. A initially invests $50,000 and adds another $10,000 after one year. B initially invests $50,000 and withdraws $10,000 after 6 months. C invests $60,000. If the profit at the end of 2 years is $84,000, what is B's share?

a) $24,000

b) $28,000

c) $30,000

d) $32,000

### Answer:

b) $28,000

### Explanation:

```
A's investment = $50,000 for 1 year + $60,000 for next 1 year.
B's investment = $50,000 for 6 months + $40,000 for next 18 months.
C's investment = $60,000 for 2 years.
Calculate the ratio and find B's share from the total profit.
```

## 19. X and Y start a business with investments of $12,000 and $16,000. After 4 months, Z joins them with a capital of $20,000. The profit at the end of the year is $9,600. Find Z's share of the profit.

a) $2,400

b) $3,200

c) $4,000

d) $4,800

### Answer:

c) $4,000

### Explanation:

```
X:Y:Z = 12000×12 : 16000×12 : 20000×8.
Calculate the ratio and find Z's share from the total profit.
```

## 20. In a partnership, A invests $10,000 for the whole year. B joins him with $20,000 after 3 months. If the profit at the end of the year is $9,000, what is B’s share?

a) $2,250

b) $3,000

c) $3,750

d) $4,500

### Answer:

b) $3,000

### Explanation:

```
A’s investment for 12 months = $10,000 × 12.
B’s investment for 9 months = $20,000 × 9.
Ratio of their investments = 10000×12 : 20000×9 = 1:1.5.
B's share = $9,000 × (1.5/2.5) = $5,400.
```