1. A, B and C are partners in a business partnership. A invested Rs. 4000 for whole year. B invested Rs. 6000 initially but increased this investment up to Rs. 8000 at the end of 4 months, while C invested Rs. 8000 initially, but withdraw Rs. 2000 at the end of 9 months. At the end of year total earned profit is Rs. 16950, find their share of profit ?

a) Rs. 3600, Rs. 6600, Rs. 6750

b) Rs. 2000, Rs. 3050, Rs. 5400

c) Rs. 2450, Rs. 2460, Rs. 1456

d) None of these

Explanation: Total capital invested by A in 1 year

$$\eqalign{ & = 12 \times 4000 \cr & = {\text{Rs}}{\text{. 48000}} \cr} $$

Total capital invested by B in 1 year

$$\eqalign{ & = 4 \times 6000 + 8 \times 8000 \cr & = 24000 + 64000 \cr & = {\text{Rs}}{\text{.}}\,{\text{88000}} \cr} $$

Total capital invested by C in 1 year

$$\eqalign{ & = 9 \times 8000 + 3 \times 6000 \cr & = 72000 + 18000 \cr & = {\text{Rs}}{\text{. 90000}} \cr} $$

A | : | B | : | C | |

Capital | 48000 | : | 88000 | : | 90000 |

24 | : | 44 | : | 45 |

$$\left( {24 + 44 + 45} \right){\text{units}}$$ = $${\text{Rs}}{\text{.}}\,{\text{16950}}$$

$$\eqalign{ & {\text{113 units}} = {\text{Rs}}{\text{. 16950}} \cr & 1{\text{ unit}} = \frac{{16950}}{{113}}{\text{ = Rs}}{\text{. 150}} \cr & {\text{Profit of A}} = 150 \times 24 = {\text{Rs}}{\text{.}}\,{\text{3600}} \cr & {\text{Profit of B}} = 150 \times 44 = {\text{Rs}}{\text{.}}\,{\text{6600}} \cr & {\text{Profit of C}} = 150 \times 45 = {\text{Rs}}{\text{.}}\,{\text{6750}} \cr} $$

2. Out of total capital required to start a business A invested 30%, B invested $$\frac{2}{5}$$ th and C invested the remaining capital. At the end of one year sum of Rs. 4000 is earned as a profit which is 20% of the capital given by B, then find how much C invested in the business ?

a) Rs. 25000

b) Rs. 10000

c) Rs. 15000

d) Rs. 12450

Explanation: Total profit = Rs. 4000

$$\eqalign{ & {\text{20% of B's capital}} = {\text{Rs}}{\text{.}}\,{\text{4000}} \cr & {\text{1% of B's capital}} = {\text{Rs}}{\text{.}}\,\frac{{{\text{4000}}}}{{20}} \cr & {\text{B's total capital}} \cr & = {\text{Rs}}{\text{. }}\frac{{{\text{4000}}}}{{20}} \times 100 \cr & = {\text{Rs}}{\text{. }}20000 \cr} $$

Let total capital required for business = 100 units.

A | : | B | : | C | |

Capital | 30 | : | 40 | : | 30 |

× 500 | : | × 500 | : | × 500 | |

15000 | : | 20000 | : | 15000 |

3. A and B started a business in partnership by investing in the ratio of 7 : 9. After 3 months A withdraw $$\frac{2}{3}$$ of its investment and after 4 months from the beginning B withdraw $$33\frac{1}{3}$$ % of its investment. If a total earned profit is Rs. 10201 at the end of 9 months, find the share of each in profit ?

a) Rs. 3535, Rs. 6666

b) Rs. 3055, Rs. 5555

c) Rs. 4503, Rs. 1345

d) Rs. 3545, Rs. 3333

Explanation: Note :In such type of question we can assume ratio as per our need to avoid fraction

Capital → | A 7 × 3 |
: | B 9 × 3 |

New Ratio, → | A 21x |
: | B 27x |

Total capital invested by A in 9 months

$$\eqalign{ & = 21x \times 3 + 7x \times 6 \cr & = 105x \cr} $$

Total capital of B invested in 9 months

$$\eqalign{ & = 27x \times 4 + 18x \times 5 \cr & = 198x \cr} $$

$$\eqalign{ & \left( {105x + 198x} \right) = {\text{Rs}}{\text{. 10201}} \cr & 303x = {\text{Rs}}{\text{. 10201}} \cr & x = \frac{{10201}}{{303}} \cr & {\text{Share of A}} = 105 \times \frac{{10201}}{{303}} = {\text{Rs}}{\text{.}}\,3535 \cr & {\text{Share of B}} = 198 \times \frac{{10201}}{{303}} = {\text{Rs}}{\text{.}}\,{\text{6666}} \cr} $$

4. A, B and C enter into a partnership, investing Rs. 6000. A invests Rs. 1000 and B and C in invests in the ratio of 2 : 3. Find the profit of C, when the annual profit is Rs. 2400 ?

a) Rs. 600

b) Rs. 1200

c) Rs. 1800

d) Rs. 1950

Explanation:

$$\eqalign{ & {\text{investment of A}} = 1000 \cr & {\text{So, investment of B}} + {\text{C}} = {\text{6000}} - 1000 \cr & = 5000 \cr & {\text{B}}:{\text{C}} = 5000 \cr & 2:3 = 2000:3000 \cr} $$

A | : | B | : | C |

1000 | : | 2000 | : | 3000 |

1 | : | 2 | : | 3 = 6 |

$$\eqalign{ & {\text{Profit of C}} = \frac{3}{6} \times 2400 = 1200 \cr} $$

5. 3 brothers divided 1620 among them in such a way that the share of second is equal to $$\frac{5}{{13}}$$ of share of other two, combined. What is the share of the second one ?

a) Rs. 1170

b) Rs. 450

c) Rs. 540

d) Rs. 500

Explanation:

$$\eqalign{ & {\text{Given share of }}{{\text{2}}^{{\text{nd}}}} \cr & = \frac{5}{{13}}{\text{of}}\left( {{{\text{1}}^{{\text{st}}}} + {{\text{3}}^{{\text{rd}}}}} \right) \cr & {\text{or, }}\frac{{{{\text{2}}^{{\text{nd}}}}}}{{{{\text{1}}^{{\text{st}}}}{\text{ + }}{{\text{3}}^{{\text{rd}}}}}} = \frac{5}{{13}} \cr & \therefore {1^{{\text{st}}}} + {{\text{2}}^{{\text{nd}}}} + {{\text{3}}^{{\text{rd}}}} = 13 + 5 = 18 \cr & 18{\text{units}} = 1620 \cr & {\text{1 unit}} = \frac{{1620}}{{18}} \cr & 5{\text{ units}} = \frac{{1620}}{{18}} \times {\text{5}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 4{\text{50}} \cr & {\text{Share of }}{{\text{2}}^{{\text{nd}}}} = {\text{Rs}}{\text{.}}\,{\text{450}} \cr} $$

6. Nonad, Vikas and and Manav enter into a partnership. Ninad invest some amount at the beginning. Vikas invest double the amount after 6 months and Manav invests thrice the amount invested by Ninad after 8 months. They earn a profit of Rs. 45000 at the end of the year. What is Manav's share in the profit ?

a) Rs. 9000

b) Rs. 12000

c) Rs. 15000

d) Rs. 25000

Explanation:

$$\eqalign{ & {\text{Let Ninad's investment be Rs}}{\text{.}}x \cr & {\text{Ratio of capitals}} = \left( {x \times 12} \right):\left( {2x \times 6} \right):\left( {3x \times 4} \right) \cr & = 12x:12x:12x \cr & = 1:1:1 \cr & {\text{Manav's share}} = {\text{Rs}}{\text{.}}\left( {45000 \times \frac{1}{3}} \right) \cr & = {\text{Rs}}{\text{.15000}} \cr} $$

7. Four milkmen rented a pasture. A grazed 15 cows for 4 months, B grazed 12 cows for 2 months, C grazed 18 cows for 6 months and D grazed 16 cows for 5 months. If A's share of rent is Rs. 1020, what is C's share of rent ?

a) Rs. 916

b) Rs. 1360

c) Rs. 1836

d) Cannot be determined

Explanation:

$$\eqalign{ & = {\text{A}}:{\text{B}}:{\text{C}}:{\text{D}} \cr & = 15 \times 4:12 \times 2:18 \times 6:16 \times 5 \cr & = 60:24:108:80 \cr & = 15:6:27:20 \cr & {\text{Let the total rent be Rs}}{\text{.}}x \cr & {\text{A's share}} = {\text{Rs}}{\text{.}}\left( {\frac{{15x}}{{68}}} \right) \cr & \therefore \,\frac{{15x}}{{68}} = 1020 \cr & x = \left( {\frac{{1020 \times 68}}{{15}}} \right) \cr & x = 4624 \cr & {\text{C's share}} = {\text{Rs}}{\text{.}}\left( {4624 \times \frac{{27}}{{68}}} \right) \cr & = {\text{Rs}}{\text{.}}\,{\text{1836}} \cr} $$

8. A, B and C are three partners in a business. The profit share of A is $$\frac{3}{{16}}$$ of the total profit and B's share is $$\frac{1}{{4}}$$ of the total profit. If C receives Rs. 243, then the amount received by B will be ?

a) Rs. 90

b) Rs. 96

c) Rs. 108

d) Rs. 120

Explanation:

$$\eqalign{ & {\text{Let total profit}} = {\text{16 units }} \cr & {\text{Profit share of A}} = \frac{3}{{16}} \times 16{\text{ units}} \cr & = 3{\text{ units}} \cr & {\text{profit share of B }} {\text{ = }}\frac{1}{4} \times 16 = 4{\text{ units}} \cr & {\text{then profit share of C}} \cr & = \left[ {16 - \left( {4 + 3} \right)} \right] = 9{\text{ units}} \cr & {\text{But profit of C}} = {\text{Rs}}{\text{. 243 (given)}} \cr & {\text{9 units}} = {\text{Rs}}{\text{. 243}} \cr & {\text{1 unit}} = {\text{Rs}}{\text{. 27}} \cr & {\text{Profit share of B}} \cr & = 4{\text{ units}} \cr & = 27 \times 4 \cr & = {\text{Rs}}{\text{. 108}} \cr} $$

9. A is a active partner and B is a inactive partner in business. A puts in Rs. 5000 and B puts in Rs. 6000. A received 15% of the profit for managing the business and the rest is divided in proportion to their capitals. The amounts received by A out of the profit of Rs. 880 in all is ?

a) Rs. 132

b) Rs. 340

c) Rs. 472

d) Rs. 492

Explanation: Total profit = Rs. 880

Since A gets 15% of total profit for management

Remaining profit

$$\eqalign{ & = 880 - \frac{{880 \times 15}}{{100}} \cr & = {\text{Rs}}.\,748 \cr} $$

A | B | ||

Amount | 5000 | 6000 | |

Ratio of Capital | 5 | : | 6 |

The remaining profit is being divided in the ratio of their capital

A's share of profit

$$\eqalign{ & = \frac{{748}}{{\left( {5 + 6} \right)}} \times 5 \cr & = {\text{Rs}}.\,340 \cr} $$

Total profit received by A = 340 + 132

= Rs. 472

10. A, B and C are partners in a business. Their shares are in the proportion of $$\frac{1}{3}:\frac{1}{4}:\frac{1}{5}$$ . A withdraws half of his capital after 15 months and after another 15 months, a profit of Rs. 4340 is divided. The share of C is ?

a) Rs. 1240

b) Rs. 1245

c) Rs. 1360

d) Rs. 1550

Explanation: Ratio of initial investments

$$\eqalign{ & = \frac{1}{3}:\frac{1}{4}:\frac{1}{5} \cr & = 20:15:12 \cr} $$

Let their initial investments be 20x, 15x and 12x respectively

= A : B : C

= (20x × 15 + 10x × 15) : (15x × 30) : (12x × 30)

= 450x : 450x : 360x

= 5 : 5 : 4

$$\eqalign{ & {\text{C's share}} = {\text{Rs}}{\text{.}}\left( {4340 \times \frac{4}{{14}}} \right) \cr & = {\text{Rs}}{\text{.1240}} \cr} $$