1. A, B, C subscribe Rs. 50,000 for a business. A subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 35,000, A receives

a) Rs. 8400

b) Rs. 13,600

c) Rs. 11,900

d) Rs. 14,700

Explanation:

Let C = x.

Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000

So, x + x + 5000 + x + 9000 = 50000

⇒ 3x = 36000

⇒ x = 12000

A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12

$$\eqalign{ & {\text{So A's Share}} \cr & = {\text{Rs}}{\text{. 3}}5000 \times \frac{{21}}{{50}} \cr & = {\text{Rs}}{\text{. 14700}} \cr} $$

2. A and B entered into partnership with capitals in the ratio 4 : 5. After 3 months, A withdrew $$\frac{1}{4}$$ of his capital and B withdrew $$\frac{1}{5}$$ of his capital. The gain at the end of 10 months was Rs. 760. A's share in this profit is:

a) Rs. 360

b) Rs. 330

c) Rs. 430

d) Rs. 380

Explanation:

$$A:B$$

$$ = \left[ {4x \times 3 + \left( {4x - \frac{1}{4} \times 4x} \right) \times 7} \right]$$ $$:$$ $$\left[ {5x \times 3 + \left( {5x - \frac{1}{5} \times 5x} \right) \times 7} \right]$$

$$\eqalign{ & = \left( {12x + 21x} \right):\left( {15x + 28x} \right) \cr & = 33x:43x = 33:43 \cr & \therefore {\text{A's share}} = {\text{Rs}}{\text{.}}\left( {760 \times \frac{{33}}{{76}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,330 \cr} $$

3. A, B and C enter into a partnership in the ratio $$\frac{7}{2}$$ : $$\frac{4}{3}$$ : $$\frac{6}{5}$$. After 4 months, A increases his share 50%. If the total profit at the end of one year be Rs. 21,600, then B's share in the profit is:

a) Rs. 2100

b) Rs. 3600

c) Rs. 4000

d) Rs. 2400

Explanation:

Ratio of initial investments

$$\eqalign{ & = {\frac{7}{2}:\frac{4}{3}:\frac{6}{5}} \cr & = 105:40:36 \cr} $$

Let the initial investments be 105x, 40x and 36x

$$\left( {105x \times 4 + \frac{{150}}{{100}} \times 105x \times 8} \right)$$ $$:$$ $$\left( {40x \times 12} \right)$$ $$:$$ $$\left( {36x \times 12} \right)$$

$$\eqalign{ & = 1680x:480x:432x \cr & = 35:10:9 \cr & {\text{Hence,}}{\kern 1pt} {\text{B's}}{\kern 1pt} {\text{share}} \cr & = {\text{Rs}}{\text{.}}\left( {21600 \times \frac{{10}}{{54}}} \right) \cr & = {\text{Rs}}{\text{.}}\,4000 \cr} $$

4. Aman started a business investing Rs. 70,000. Rakhi joined him after six months with an amount of Rs. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business?

a) 12 : 15 : 16

b) 42 : 45 : 56

c) 7 : 6 : 10

d) Cannot be determined

Explanation:

Aman : Rakhi : Sagar

= (70,000 x 36) : (1,05,000 x 30) : (1,40,000 x 24)

= 12 : 15 : 16

5. A, B, C rent a pasture. A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing. If the rent of the pasture is Rs. 175, how much must C pay as his share of rent?

a) Rs. 45

b) Rs. 55

c) Rs. 50

d) Rs. 60

Explanation:

$$\eqalign{ & A:B:C \cr & = \left( {10 \times 7} \right):\left( {12 \times 5} \right):\left( {15 \times 3} \right) \cr & = 70:60:45 \cr & = 14:12:9 \cr & \therefore {\text{C's}}\,{\text{rent}} = Rs.\,\left( {175 \times \frac{9}{{35}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,45 \cr} $$

6. P, Q, R enter into a partnership. P initially invests 25 lakh & adds another 10 lakhs after one year. Q initially invests 35 lakh & withdrawal 10 lakh after 2 years and R invests Rs 30 Lakhs. In what ratio should the profit be divided at the end of 3 years?

a) 18 : 18 : 19

b) 19 : 19 : 18

c) 18 : 19 : 19

d) 18 : 19 : 18

Explanation:

P : Q : R

= (25 × 1 + 35 × 2) : (35 × 2 : 25 × 1) : (30 × 3)

= 95 : 95 : 90

= 19 : 19: 18

7. A began a business with Rs. 85,000. He was joined afterwards by B with Rs. 42,500. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1?

a) 6 months

b) 5 months

c) 4 months

d) 8 months

Explanation:

$$\eqalign{ & {\text{Suppose}}\,{\text{B}}\,{\text{joined}}\,{\text{for}}\,x\,{\text{months}}. \cr & {\text{Then}}, \cr & {\frac{{85000 \times 12}}{{42500 \times x}} = \frac{3}{1}} \cr & \Rightarrow x = {\frac{{85000 \times 12}}{{42500 \times 3}}} = 8 \cr & {\text{So,}}\,{\text{B}}\,{\text{joined}}\,{\text{for}}\,{\text{8}}\,{\text{months}} \cr} $$

8. A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Rs. 6500 for 6 months, B, Rs. 8400 for 5 months and C, Rs. 10,000 for 3 months. A wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Rs. 7400. Calculate the share of B in the profit.

a) Rs. 2840

b) Rs. 1900

c) Rs. 2660

d) Rs. 2800

Explanation:

For managing, A received = 5% of Rs. 7400 = Rs. 370.

Balance = Rs. (7400 - 370) = Rs. 7030.

Ratio of their investments = (6500 x 6) : (8400 x 5) : (10000 x 3)

= 39000 : 42000 : 30000

= 13 : 14 : 10

$$\eqalign{ & \therefore {\text{ B's Share}} \cr & = {\text{Rs}}{\text{. 7030}} \times \frac{{14}}{{37}} \cr & = {\text{Rs}}{\text{. 2660}} \cr} $$

9. A and B started a business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, C joined them with Rs. 20,000. What will be B's share in total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business?

a) Rs. 7500

b) Rs. 10,000

c) Rs. 9500

d) Rs. 9000

Explanation:

A : B : C

= (20,000 × 24) : (15,000 × 24) : (20,000 × 18)

= 4 : 3 : 3.

$$\eqalign{ & {\text{So B's Share}} \cr & = {\text{Rs}}{\text{. }}25000 \times \frac{3}{{10}} \cr & = {\text{Rs}}{\text{. 7500}} \cr} $$

10. Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 24,500. What was Simran's share in the profit?

a) Rs. 9,423

b) Rs. 10,250

c) Rs. 10,500

d) Rs. 12,500

Explanation:

$$\eqalign{ & {\text{Simran}}\,{\text{:}}\,{\text{Nanda}} \cr & = \left( {50000 \times 36} \right):\left( {80000 \times 30} \right) \cr & = 3:4 \cr & \therefore {\text{Simran's}}\,{\text{share}} \cr & = Rs.\,\left( {24500 \times \frac{3}{7}} \right) \cr & = Rs.\,10,500 \cr} $$