1. Yogesh started a business investing Rs. 45000. After 3 months, Pranab joined him with a capital of Rs. 60000. After another 6 months, Atul joined them with a capital of Rs. 90000. At the end of the year, they made a profit of Rs. 20000. What would be Atuls share in it?

a) Rs. 7000

b) Rs. 6000

c) Rs. 5000

d) Rs. 4000

Explanation: Yogesh : Pranab : Atul

= 45000 × 12 : 60000 × 9 : 90000 × 3

= 2 : 2 : 1

Atul's share

$$\eqalign{ & = {\text{Rs}}{\text{. }}20000 \times \frac{1}{5} \cr & = {\text{Rs}}{\text{. }}4000 \cr} $$

2. Rahul and Bharti are partners in a business. Rahul contributes $$\frac{1}{4}$$th capital for 15 months and Bharti received $$\frac{2}{3}$$ of profit. For how long Bharti money was used

a) 8 months

b) 10 months

c) 11 months

d) 17 months

Explanation:

$$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{total}}\,{\text{profit}}\,{\text{be}}\,Rs.\,Z \cr & {\text{Bharti's}}\,{\text{share}} = {\frac{2}{3}} Z \cr & {\text{Rahul's}}\,{\text{share}} = Z - {\frac{2}{3}} Z \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{Z}{3} \cr & {\text{Rahul:Bharti}} \cr & = \frac{Z}{3}: {\frac{2}{3}} Z = 1:2 \cr & {\text{Now}}\,{\text{let}}\,{\text{the}}\,{\text{total}}\,{\text{capital}}\,{\text{be}}\,Rs\,X, {\text{and}}\,{\text{Bharti}}\,{\text{capital}}\,{\text{was}}\,{\text{used}}\,{\text{for}}\,Y\,{\text{months}}. \cr & {\text{then,}}\,{\text{Rahul}}\,{\text{capital}}\,{\text{will}}\,{\text{be}}\, {\frac{1}{4}} X \cr & {\text{and}}\,{\text{Bharti}}\,{\text{capital}}\,{\text{will}}\,{\text{be}}\,X - {\frac{1}{4}} X \cr & = \frac{{3X}}{4} \cr & \frac{{\frac{1}{4}X*15}}{{\frac{3}{4}X*Y}} = \frac{1}{2} \cr & Y = \frac{{15*2}}{3} = 10 \cr} $$

3. P and Q started a business investing Rs. 85000 and Rs. 15000 resp. In what ratio the profit earned after 2 years be divided between P and Q respectively.

a) 17 : 5

b) 17 : 3

c) 17 : 6

d) 17 : 7

Explanation: P : Q = 85000 : 15000

= 85 : 15

= 17 : 3

4. A, B and C enter into a partnership investing Rs 35000, Rs 45000 and Rs 55000 resp. The respective share of A,B and C in an annual profit of Rs 40500 are.

a) Rs. 11500, Rs. 13500, Rs. 16500

b) Rs. 10500, Rs. 12500, Rs. 16500

c) Rs. 10500, Rs. 13500, Rs. 15500

d) Rs. 10500, Rs. 13500, Rs. 16500

Explanation:

$$\eqalign{ & A:B:C \cr & = 35000:45000:55000 \cr & = 7:9:11 \cr & {\text{Now}}\,{\text{we}}\,{\text{are}}\,{\text{having}}\,{\text{the}}\,{\text{ratio}}\, {\text{to}}\,{\text{get}}\,{\text{the}}\,{\text{share,}}\,{\text{first}}\,{\text{make}}\,{\text{total}}\,{\text{of}}\,{\text{above}}\,{\text{ratio}}\, {\text{then}}\,{\text{get}}\,{\text{each}}\,{\text{share}}{\text{.}} \cr & {\text{A's}}\,{\text{Share}} = 40500*\frac{7}{{27}} = Rs.\,10500 \cr & {\text{B's}}\,{\text{Share}} = 40500*\frac{9}{{27}} = Rs.\,13500 \cr & {\text{C's}}\,{\text{Share}} = 40500*\frac{{11}}{{27}} = Rs.\,16500\, \cr} $$

5. Rahul, Arun and Sumit started a business. Rahul invested $$\frac{1}{2}$$ part, Arun $$\frac{1}{3}$$ part and rest of the capital was invested by Sumit. The ratio of their profits will be = ?

a) 2 : 3 : 1

b) 3 : 2 : 1

c) 2 : 3 : 6

d) 3 : 2 : 5

Explanation: Let total capital be Rs. x

$$\eqalign{ & {\text{Rahul's share}} = {\text{Rs}}{\text{.}}\frac{x}{2} \cr & {\text{Arun's share}} = {\text{Rs}}{\text{.}}\frac{x}{3} \cr & {\text{Sumit's share}} \cr & = {\text{Rs}}{\text{.}}\left[ {x - \left( {\frac{x}{2} + \frac{x}{3}} \right)} \right] \cr & = {\text{Rs}}{\text{. }}\frac{x}{6} \cr & {\text{Required ratio}} \cr & = \frac{x}{2}:\frac{x}{3}:\frac{x}{6} \cr & = \frac{1}{2}:\frac{1}{3}:\frac{1}{6} \cr & = 3:2:1 \cr} $$

6. A, B and C subscribe Rs. 50000 for a business. A subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 35000, A receives ?

a) Rs. 8400

b) Rs. 11900

c) Rs. 13600

d) Rs. 14700

Explanation:

$$\eqalign{ & {\text{Let C}} = x \cr & {\text{B}} = x + 5000{\text{ and}} \cr & {\text{A}} = x + 5000 + 4000 = x + 9000 \cr & \Rightarrow x + x + 5000 + x + 9000 = 50000 \cr & 3x = 36000 \cr & x = 12000 \cr & {\text{A}}:{\text{B}}:{\text{C}} \cr & = 21000:17000:12000 \cr & = 21:17:12 \cr & {\text{A's share}} = {\text{Rs}}{\text{.}}\left( {35000 \times \frac{{21}}{{50}}} \right) \cr & = {\text{Rs.}}{\text{14700}} \cr} $$

7. A, B and C are three partners. They altogether invested Rs. 14000 in business. At the end of the year, A got Rs. 337.50, B Rs. 1125 and C Rs. 637.50 as profit. The difference between the investments of B and A was ?

a) Rs. 2200

b) Rs. 3200

c) Rs. 4200

d) Rs. 5250

Explanation: Ratio of investments of A, B and C = Ratio of their profits

$$\eqalign{ & = 337.50:1125:637.50 \cr & = 9:30:17 \cr & {\text{A's investment}} = {\text{Rs}}{\text{.}}\left( {14000 \times \frac{9}{{56}}} \right) \cr & = {\text{Rs. }}{\text{2250}} \cr & {\text{B's investment}} = {\text{Rs}}{\text{.}}\left( {14000 \times \frac{{30}}{{56}}} \right) \cr & = {\text{Rs. }}{\text{7500}} \cr & {\text{Required difference}} = {\text{Rs}}{\text{.}}\left( {7500 - 2250} \right) \cr & = {\text{Rs. }}{\text{5250}} \cr} $$

8. A and B are two partners in a firm sharing the profit in the ratio 4 : 5. If the firm earns a profit of Rs. 14130, then profit to be received by B ?

a) Rs. 6280

b) Rs. 7850

c) Rs. 1570

d) Rs. 3140

Explanation:

$$\eqalign{ & {\text{A}}:{\text{B}} \cr & 4:{\text{ }}5 \cr & \left( {4 + 5} \right){\text{units}} = {\text{Rs}}{\text{. 14130}} \cr & {\text{1 unit}} = \frac{{14130}}{9} = {\text{Rs}}{\text{. }}1570 \cr & 5{\text{ units}} = 5 \times 1570 = {\text{Rs}}{\text{. 7850}} \cr & {\text{Share of B}} = {\text{Rs}}{\text{. 7850}} \cr} $$

9. A and B started a business investing amounts in the ratio of 2 : 3. If A has invested an additional amount of Rs. 10000, their ratio of investment would have been 3 : 2. The amount invested by A was ?

a) Rs. 8000

b) Rs. 12000

c) Rs. 18000

d) Rs. 20000

Explanation: Initial ratio of investments by A and B = 2 : 3

Let their respective investments are 2x and 3x

If A added Rs. 10000 to his investment

Then the new ratio = 3 : 2

$$\eqalign{ & \frac{{2x + 10000}}{{3x}} = \frac{3}{2} \cr & 4x + 20000 = 9x \cr & 5x = 20000 \cr & x = 4000 \cr} $$

Original investment by A = 2 × 4000 = Rs. 8000

10. A, B and C started a business investing amounts in the ratio of 5 : 6 : 8 respectively. After one year, C withdrew 50% of the amount and A invested an additional amount of 60% of the original amount invested by him. In what ratio, the profit earned at the end of 2 years should be distributed among A, B and C respectively ?

a) 2 : 3 : 3

b) 4 : 3 : 2

c) 13 : 12 : 12

d) Cannot be determined

Explanation: Let the initial investments of A, B and C be Rs. 5x, Rs. 6x and Rs. 8x respectively

A : B : C

[5x × 12 + (160% of 5x) × 12] : (6x × 24) : (8x × 12 + 4x × 12)

= 156x : 144x : 144x

= 13 : 12 : 12