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**Question 1: **A, B and C started a business by investing Rs. 20,000 Rs. 28,000 and Rs. 36,000 respectively. After 6 months, A and B withdrew an amount of Rs. 8,000 each and C invested an additional amount of Rs. 8,000. All of them invested for equal period of time. If at the end of the year. C got Rs. 12,550 as his share of profit, what was the total profit earned ?

a) Rs. 25,100

b) Rs. 26,600

c) Rs. 24,300

d) Rs. 22,960

e) Rs. 21,440

**Question 2: **Sarita started a boutique investing an amount of Rs. 50,000. Six months later Neeta joined her with an amount of Rs. 80,000. At the end of one year they earned a profit of Rs. 18,000. What is Sarita’s share in the profit?

a) Rs. 9000

b) Rs. 8000

c) Rs. 12000

d) Rs. 10000

e) None of these

**Question 3: **Prabha started a business investing Rs. 32,000. After 5 months Amit joined her with a capital of Rs. 22,000. At the end of the year the total profit was Rs. 16,409. What is Prabha’s share in the profit ?

a) Rs. 5,284

b) Rs. 11,712

c) Rs. 10,182

d) Rs. 4,697

e) None of these

**Question 4: **A and B both start a small business with an investment of Rs. 3500 and Rs. 4000 respectively. At the end of few months from the start of the business, A withdrew from the business completely and B remained for the year. If the annual profit was divided between A and B in the respective ratio of 7 : 12, then after how many months from the start of the business, did A leave the business?

a) Eight

b) Nine

c) Ten

d) Five

e) Seven

**Question 5: **Abhijit invested in three schemes A, B and C the amounts in the ratio of 2 : 3 : 4 respectively. If the schemes offered interest @ 20 p.c.p.a. 16 p.c.p.a. and 15 p. c.p. a. respectively, what will be the respective ratio of the amounts after one year ?

a) 10 : 8 : 5

b) 12 : 14 : 15

c) 12 : 15 : 22

d) Cannot be determined

e) None of these

**Question 6: **A, B and C entered into a partnership by investing Rs.64000, Rs. 52000 and Rs. 36000 respectively for a certain period of time. If A receives Rs.35584 as annual profit, what amount will Mr. C receive as his share in the profit ?

a) Rs. 20632

b) Rs.18296

c) Rs. 21084

d) Rs. 19768

e) Rs. 20016

**Question 7: **A, B and C together start a business. The ratio of investment of A and B is 7 : 8 and that of B and C is 4 : 9. B gets a share of Rs. 7104 in annual profit. What is C’s share in the profit ?

a) Rs. 16984

b) Rs. 16894

c) Rs. 15894

d) Rs. 14894

e) None of these

**Question 8: **A, B and C started a business together. The respective ratio of investment of A and B was 7:9 and that of B and C was 18:11. All of them invested for equal period of time. If the total profit earned by them was Rs. 15,050. what was C’s share of profit?

a) Rs. 3,850

b) Rs. 4,350

c) Rs. 4,150

d) Rs. 3,700

e) Rs. 3,650

**Question 9: **Raj and Prithvi both started a business together, in which Raj invests X and Prithvi invests (X + 2000). At the end of one year, the total profit earned was 8,400, from which Raj’s share was 3,600/ How much had Prithvi invested in the business ?

a) 16,400/-

b) 12,000/-

c) 12,500/-

d) 8,000/-

e) 16,000/-

**Question 10: **A and B started a business with initial investments in the ratio 5 : 7. If after one year their profits were in the ratio 1 : 2 and the period for A’s investment was 7 months, B invested the money for :

a) 6 months

b) 2 1/2 months

c) 10 months

d) 4 months

e) 7 months

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**Question 11: **A and B start a business together with an investment of Rs. 3,000/and Rs. 6,000/ respectively. At the end of six months from the start of the business, B withdrew half of his investment. If at the end of the year, B’s share from the total profit earned was Rs. 3,750/, what was the total profit earned ?

a) Rs. 5,750/

b) Rs. 6,250/

c) Rs. 6,500/

d) Rs. 6,400

e) None of these

**Question 12: **Pihu and Rani start a business together by investing Rs.9 ,000/-and Rs.6,300/- respectively. After a certain period, Pihu withdrew from the business completely. If at the end of 2 years the total profit earned was Rs.13,050/- and Pihu’s share was Rs.6,750/-, after how many months did Pihu withdraw from business ?

a) 23 months

b) 14 months

c) 20 months

d) 18 months

e) 12 months

**Question 13: **Raksha invested an amount of Rs. 60,000 to start a software business. After six months, Kamal joined her with an amount of Rs. 90,000. After one year from the commencement of the business, Raksha put in an additional amount of Rs. 20,000. At the end of three years, they earned a profit of Rs. 71,20,000. What is Raksha’s share in the profit ?

a) Rs. 35,20,000

b) Rs. 26,40,000

c) Rs. 27,00,000

d) Rs. 38,40,000

e) None of these

**Question 14: **A, B and C together start a business. The ratio of the investments of A, B and C is 0.125 : 0.75 : 0.25. After 8 months A adds thrice amount of his earlier investment and C withdraws half of his earlier investment. At the end of the year, they earn a total profit of Rs. 5800. What is B’s share in the profit ?

a) Rs. 3400

b) Rs. 3200

c) Rs. 3600

d) Rs. 3800

e) None of these

**Question 15: **A, B and C started a business by investing Rs.8,400/, Rs.15,600/ and Rs.13,200/ respectively.All of them invested for equal period of time. If A’s share of annual profit was Rs.1,960/, what was the difference B’s share of annual profit and C’s share of annual profit ?

a) Rs. 560/

b) Rs. 520/

c) Rs. 540/

d) Rs. 480/

e) Rs. 600/

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**Answers & Solutions:**

**1) Answer (A)**

Amount invested by A,B and C = Rs. 20,000 Rs. 28,000 and Rs. 36,000 respectively.

Ratio of profits shared by A : B : C

= $[(20,000 \times 6) + (12,000 \times 6)]$ : $[(28,000 \times 6) + (20,000 \times 6)]$ : $[(36,000 \times 6) + (44,000 \times 6)]$

= $32 : 48 : 80 = 2 : 3 : 5$

Let total profit earned = $Rs. x$

Profit received by C = $\frac{5}{(2 + 3 + 5)} \times x = 12550$

=> $\frac{x}{2} = 12550$

=> $x = 12550 \times 2 = Rs. 25,100$

**2) Answer (D)**

Amount invested by Sarita = Rs. 50,000 and amount invested by Neeta = Rs. 80,000

Ratio of amount invested by Sarita : Neeta = 5 : 8

Time period in which Sarita invested = 12 months and Neeta = 6 months

Ratio of time periods of Sarita : Neeta = 2 : 1

=> Ratio of profits earned by Sarita : Neeta = $(5 \times 2)$:$(8 \times 1)$

= 5 : 4

Total profit earned = Rs. 18,000

$\therefore$ Sarita’s share in the profit = $\frac{5}{(5+4)} \times 18,000$

= $5 \times 2,000 = Rs. 10,000$

=> Ans – (D)

**3) Answer (B)**

Amount invested by Prabha = Rs. 32,000 and amount invested by Amit = Rs. 22,000

Ratio of amount invested by Prabha : Amit = 16 : 11

Time period in which Prabha invested = 12 months and Amit =76 months

Ratio of time periods of Prabha : Amit = 12 : 7

=> Ratio of profits earned by Prabha : Amit = $(16 \times 12)$:$(11 \times 7)$

= 192 : 77

Total profit earned = Rs. 16,409

$\therefore$ Prabha’s share in the profit = $\frac{192}{(192+77)} \times 16,409$

= $192 \times 61 = Rs. 11,712$

=> Ans – (B)

**4) Answer (A)**

Let A remained in the business for $x$ months.

Amount invested by A = Rs. 3500

Amount invested by B = Rs. 4000

Ratio of share in profit received by A and B

=> $\frac{3500 \times x}{4000 \times 12} = \frac{7}{12}$

=> $\frac{7 x}{8 \times 12} = \frac{7}{12}$

=> $x = 8$

$\therefore$ 8 months from the start of the business A left the business.

**5) Answer (E)**

Let the amount invested in schemes A, B and C in Rs. respectively be $2x , 3x$ and $4x$

Amount after 1 year in scheme :

A = $\frac{120}{100} \times 2x = 2.4x$

B = $\frac{116}{100} \times 3x = 3.48x$

C = $\frac{115}{100} \times 4x = 4.6x$

=> Required ratio = 2.4 : 3.48 : 4.6

= 60 : 87 : 115

**6) Answer (E)**

Ratio of shares = A : B : C

= 64000 : 52000 : 36000 = 16 : 13 : 9

$\because$ $16 \equiv 35584$

$\therefore 9 \equiv \frac{35584}{16} \times 9$

= Rs. 20,016

**7) Answer (E)**

A : B = 7 : 8

B : C = 4 : 9 = 8 : 18

=> A : B : C = 7 : 8 : 18

Let total profit be $P$

=> B’s share = $\frac{8}{33} \times P = 7104$

=> $P = \frac{7104 \times 33}{8}$

Now, C’s share = $\frac{18}{33} * P$

= $\frac{18}{33} \times \frac{7104 * 33}{8}$

= $18 * 888 = $Rs. $15,984$

**8) Answer (A)**

A : B = 7 : 9 = 14 : 18

B : C = 18 : 11

=> Ratio of investments = A : B : C = 14 : 18 : 11

Total profit = Rs. 15,050

$\therefore$ C’s share of profit = $\frac{11}{14 + 18 + 11} \times 15,050$

= $\frac{11}{43} \times 15050$

= $11 \times 350$ = Rs. $3,850$

**9) Answer (D)**

Ratio of investments of Raj and Prithvi = $x : (x + 2000)$

Total profit = Rs. 8,400

Acc to ques,

=> $\frac{x}{x + x + 2000} \times 8400 = 3600$

=> $\frac{x}{2x + 2000} = \frac{36}{84}$

=> $\frac{x}{2x + 2000} = \frac{3}{7}$

=> $7x = 6x + 6000$

=> $x = 6000$

$\therefore$ Amount invested by Prithvi = 6000 + 2000

= Rs. 8,000

**10) Answer (C)**

Let B invested the money for = $x$ months

=> Ratio of investments of A : B = $(5 \times 7) : (7 \times x)$

= $5 : x$

Acc to ques

=> $\frac{5}{x} = \frac{1}{2}$

=> $x = 5 \times 2 = 10$ months

**11) Answer (B)**

The ratio of amount invested by A and B

= $(12 \times 3,000) : (6 \times 6,000) + (6 \times 3,000)$

= $(36) : (36) + (18)$

= $36 : 54 = 2 : 3$

Let the total profit = Rs. $x$

Acc to ques,

=> B’s share = $\frac{3}{2 + 3} \times x = 3,750$

=> $x = \frac{3,750 \times 5}{3}$

=> $x = 1250 \times 5$ = Rs. $6,250$

**12) Answer (D)**

Total profit = Rs. 13,050

Pihu’s share = Rs. 6,750

=> Rani’s share = 13,050 – 6,750 = Rs. 6,300

Let Pihu withdrew after $x$ months

=> Ratio of investments of Pihu and Rani

= $(9,000 \times x) : (6,300 \times 24)$

= $5x : 84$

Acc to ques,

=> $\frac{5x}{84} = \frac{6750}{6300}$

=> $\frac{5x}{84} = \frac{15}{14}$

=> $x = \frac{15}{14} \times \frac{84}{5}$

=> $x = 3 \times 6 = 18$ months

**13) Answer (A)**

Equivalent capital of Raksha for 1 year

= Rs. (60,000 $\times$ 1 + 80,000 $\times$ 2)

= Rs. 60,000 + 1,60,000

= Rs. 2,20,000

Equivalent capital of Kamal for 1 year

= Rs. (90,000 $\times 2\frac{1}{2}$)

= Rs. 2,25,000

=> Ratio of capitals = 2,20,000 : 2,25,000

= 44 : 45

Total profit = Rs. 71,20,000

=> Raksha’s share in the profit = $\frac{44}{44 + 45} \times 71,20,000$

= $44 \times 80,000$

= Rs. $35,20,000$

**14) Answer (C)**

A : B : C = 0.125 : 0.75 : 0.25

= 125 : 750 : 250 = 1 : 5 : 2

Let investments of A, B & C be $x , 5x , 2x$ respectively

After 8 months, A added = $x + 3 * x = 4x$

and C withdraws = $\frac{2x}{2} = x$

=> Ratio of profits = A : B : C

= $(x * 8) + (4x * 4) : (6x * 12) : (2x * 8) + (x * 4)$

= $24x : 72x : 20x = 6 : 18 : 5$

Total profit = 5800

$\therefore$ B’s profit = $\frac{18}{29} * 5800$ = Rs. 3,600

**15) Answer (A)**

Investment by A, B & C = 8400, 15600 , 13200

=> A : B : C = 7 : 13 : 11

Let total profit be x

=> A’s share = $\frac{7}{31} * x = 1960$

=> $x = \frac{1960 * 31}{7} = 8680$

$\therefore$ Difference between B’s and C’s share of profit = $\frac{2}{31}$ * 8680

= Rs. 560

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