1. A, B and C enter into a partnership. A initially invests Rs. 25 lakhs and adds another Rs. 10 lakhs after one year. B initially invests Rs. 35 lakhs and withdraws Rs. 10 lakhs after 2 years and C invests Rs. 30 lakhs. In what ratio should the profits be divided at the end of 3 years ?

a) 10 : 10 : 9

b) 20 : 20 :19

c) 20 : 19 :18

d) None of these

Explanation: A : B : C

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

= 95 lakhs : 95 lakhs : 90 lakhs

= 19 : 19 : 18

2. Subhash starts a business by investing Rs. 25000. 6 months later Aditya joins him by investing Rs. 15000. After another 6 months Aditya invests an additional amount of Rs. 15000. At the end of 3 years they earn a profit of Rs. 247000. What is Aditya's share in the profit ?

a) Rs. 105000

b) Rs. 111500

c) Rs. 123000

d) Rs. 117000

Explanation:

$$\eqalign{ & {\text{Subhas}}:{\text{Aditya}} = \left( {25000 \times 36} \right):\left( {15000 \times 6 + 30000 \times 24} \right) \cr & = 900000:810000 \cr & = 10:9 \cr & {\text{Aditya's share}} = {\text{Rs}}{\text{.}}\left( {247000 \times \frac{9}{{19}}} \right) \cr & = {\text{Rs}}{\text{.117000}} \cr} $$

3. A, B and C enter into a partnership with capitals in the ratio 5 : 6 : 8. At the end of the business term, they received the profit in the ratio 5 : 3 : 12. Find the ratio of time for which they contributed their capitals ?

a) 2 : 1 : 3

b) 1 : 2 : 3

c) 2 : 3 : 1

d) 3 : 2 : 1

Explanation:

$$\eqalign{ & {\text{Here}}\,{{\text{p}}_1}:{{\text{p}}_2}:{{\text{p}}_3} = 5:3:12 \cr & {\text{and}}\,{{\text{x}}_1}:{{\text{x}}_2}:{{\text{x}}_3} = 5:6:8 \cr & {\text{Required}}\,{\text{ratio}} \cr & = \frac{{{{\text{p}}_1}}}{{{{\text{x}}_1}}}:\frac{{{{\text{p}}_2}}}{{{{\text{x}}_2}}}:\frac{{{{\text{p}}_3}}}{{{{\text{x}}_3}}} \cr & = \frac{5}{5}:\frac{3}{6}:\frac{{12}}{8} \cr & = 1:\frac{1}{2}:\frac{3}{2} \cr & = 2:1:3 \cr} $$

4. X and Z invest capital in the ratio of 2 : 1 while X and Y invest capital in the ratio of 3 : 2. If their annual profit is Rs. 157300 then what is Y share ?

a) Rs. 48400

b) Rs. 58809

c) Rs. 48810

d) Rs. 47782

Explanation: X : Z = 2 : 1

X : Y = 3 : 2

X : Z = 2 : 1 (multiply with 3)

X : Y = 3 : 2 (multiply with 2)

i.e X : Z = 6 : 3

X : Y = 6 : 4

∴ X : Y : Z = 6 : 4 : 3

(6 + 4 + 3) units = Rs.157300

13 units = Rs.157300

1 unit = Rs.12100

4 units = Rs.12100 × 4 = Rs. 48400

Share of Y = Rs. 48400

5. A and B start a business with investments of Rs. 5000 and Rs. 4500 respectively. After 4 months, A takes out half of his capital. After two more months B takes out one-third of his capital while C joins them with a capital of Rs. 7000. At the end of a year, they earn a profit of Rs. 5080. Find the share of each member in the profit ?

a) A = Rs. 1400, B = Rs. 1900, C = Rs. 1780

b) A = Rs. 1600, B = Rs. 1800, C = Rs. 1680

c) A = Rs. 1800, B = Rs. 1500, C = Rs. 1780

d) A = Rs. 1680, B = Rs. 1600, C = Rs. 1800

Explanation: A : B : C

(5000 × 4 + 2500 × 8) : (4500 × 6 + 3000 × 6) : (7000 × 6)

= 40000 : 45000 : 42000

= 40 : 45 : 42

$$\eqalign{ & {\text{A's share}} = {\text{Rs}}{\text{.}}\left( {5080 \times \frac{{40}}{{127}}} \right) \cr & = {\text{Rs}}{\text{.}}\,{\text{1600}} \cr & {\text{B's share}} = {\text{Rs}}{\text{.}}\left( {5080 \times \frac{{45}}{{127}}} \right) \cr & = {\text{Rs}}{\text{.}}\,{\text{1800}} \cr & {\text{C's share}} = {\text{Rs}}{\text{.}}\left( {5080 \times \frac{{42}}{{127}}} \right) \cr & = {\text{Rs}}{\text{.}}\,{\text{1680}} \cr} $$

6. A, B and C invested Rs. 47000 for a business. If A subscribes Rs. 7000 more than B and B Rs. 5000 more than C, then out of total profit of Rs. 4700, C receives ?

a) Rs. 1200

b) Rs. 4500

c) Rs. 1000

d) None of these

Explanation: Let C subscribes the business = Rs. x

A : B : C

Capital → (x + 12000) : (x + 5000) : x

Note: Profit would be divide in the ratio of their capitals

$$\eqalign{ & \Rightarrow \left( {x + 12000} \right) + \left( {x + 5000} \right) + x = 47000 \cr & 3x + 17000 = 47000 \cr & 3x = 30000 \cr & x = 10000 \cr & {\text{ A }}:{\text{ B }}:{\text{ C}} \cr & {\text{Capital}} \to 22000:15000:10000 \cr & {\text{Profit}} \to {\text{ }}22{\text{ }}:{\text{ }}15{\text{ }}:{\text{ }}10 \cr & \left( {22 + 15 + 10} \right){\text{ units}} = {\text{4700}} \cr & {\text{1 unit}} = \frac{{4700}}{{47}} = 100 \cr & {\text{Share of C}} = 10{\text{ units}} = 10 \times 100 = {\text{Rs}}.1000 \cr & \cr} $$

7. A and B started a business investing amount of Rs. 185000 and Rs. 225000 respectively. If B's share in the profit earned by them is Rs. 9000 then what is the total profit earned by them together ?

a) Rs. 17400

b) Rs. 16400

c) Rs. 16800

d) Rs. 17800

Explanation:

A | B | ||

Capital → | 1850000 | : | 225000 |

Profit → | 37 | : | 45 |

↓×200 | : | ↓×200 | |

7400 | 9000 |

8. A and B stared a boutique investing amounts of Rs. 35000 and Rs. 56000 respectively. If A's share in the profit earned by them need is Rs. 45000, then what is the total profit earned ?

a) Rs. 81000

b) Rs. 127000

c) Rs. 72000

d) Rs. 117000

Explanation:

A | B | ||

Capital → | 35000 | : | 56000 |

Profit → | 5 | : | 8 |

↓×9000 | : | ↓×9000 | |

45000 | 72000 |

9. Sonia started a business investing Rs. 60000. After 6 months Vivek joined him with an amount of Rs. 140000. After 1 year Kirti also joined them with Rs. 120000. After 2 years the business yielded a total profit of Rs. 450000. What is the share of Vivek in the profit ?

a) Rs. 140000

b) Rs. 198500

c) Rs. 210000

d) Rs. 215000

Explanation: Sonia : Vivek : Sagar

= (60000 × 24) : (140000 × 18) : (120000 × 12)

= 1440000 : 2520000 : 1440000

= 4 : 7 : 4

$$\eqalign{ & {\text{Vivek's share}} = {\text{Rs}}{\text{.}}\,\left( {450000 \times \frac{7}{{15}}} \right) \cr & = {\text{Rs}}{\text{. 210000}} \cr} $$

10. P and Q started a business in the ratio of 2 : 3. After 1 year P left the business but Q continues. After 2 years he had profit of Rs. 26000. What is the profit of Q?

a) Rs. 10400

b) Rs. 13000

c) Rs. 15600

d) None of these

Explanation: Let the initial capital of P and Q be Rs. 2x and Rs. 3x respectively

Ratio of profits

$$\eqalign{ & = \left( {2x \times 12} \right):\left( {3x \times 24} \right) \cr & = 24x:72x \cr & = 1:3 \cr & {\text{Q's share}} = {\text{Rs}}{\text{.}}\left( {26000 \times \frac{3}{4}} \right) \cr & = {\text{Rs. }}{\text{19500}} \cr} $$