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51. 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

Discuss

Solution:

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
According to the question,

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

52. 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

Discuss

Solution:

	A		B
Capital →	1850000	:	225000
Profit →	37	:	45
	↓×200	:	↓×200
	7400		9000

Total profit = (7400 + 9000) = Rs. 16400

53. 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

Discuss

Solution:

	A		B
Capital →	35000	:	56000
Profit →	5	:	8
	↓×9000	:	↓×9000
	45000		72000

Total profit = (45000 + 72000) = Rs. 117000

54. 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

Discuss

Solution:

Sonia : Vivek : Sagar
= (60000 × 24) : (140000 × 18) : (120000 × 12)
= 1440000 : 2520000 : 1440000
= 4 : 7 : 4

\begin{aligned} ∴ Vivek's share \\ \Rightarrow Rs . (450000 \times \frac{7}{15}) \\ \Rightarrow Rs . 210000 \end{aligned}

55. 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. Rs. 18500

Discuss

Solution:

Let the initial capital of P and Q be Rs. 2x and Rs. 3x respectively
Then, ratio of profits

\begin{aligned} = (2 x \times 12) : (3 x \times 24) \\ = 24 x : 72 x \\ = 1 : 3 \\ ∴ Q's share \\ = Rs . (26000 \times \frac{3}{4}) \\ = Rs. 19500 \end{aligned}

56. A, B and C enter into a partnership. A invests some money at the beginning, B invests double the amount after six months and C invest thrice the amount after eight months. If the annual profit be Rs. 27000; C's share (in Rs.) is ?

A. Rs. 8625

B. Rs. 9000

C. Rs. 10800

D. Rs. 11250

Discuss

Solution:

Let the money invested by A, B and C be Rs. x, Rs. 2x and Rs. 3x respectively
Then, A : B : C

\begin{aligned} = (x \times 12) : (2 x \times 6) : (3 x \times 4) \\ = 12 x : 12 x : 12 x \\ = 1 : 1 : 1 \\ ∴ C's share \\ = Rs . (27000 \times \frac{1}{3}) \\ = Rs. 9000 \end{aligned}

57. X and Y enter into a partnership with capitals in the ratio 5 : 6 and at the end of 8 months, X withdraws. If they receive profit in the ratio of 5 : 9. Find how long Y's capital was used.

A. 8 months

B. 9 months

C. 11 months

D. 12 months

Discuss

Solution:

Let the capitals of Y was used for T months
According to the question,

\begin{aligned} \frac{5 \times 8}{6 \times T} = \frac{5}{9} \\ \Rightarrow T = 12 months \end{aligned}

Hence capital of Y was used for = 12 months

58. Two partners invest Rs. 125000 and Rs. 85000 respectively in a business and agree that 60% of the profit should be divided equally between them and the remaining profit is to be divided into ratio of their capitals. If one partner gets Rs. 300 more than the other. Find the total profit made in the business ?

A. Rs. 3739.50

B. Rs. 3937.50

C. Rs. 3749.50

D. Rs. 3947.50

Discuss

Solution:

	1^st Partner		2^nd Partner
Capital →	125000	:	85000
	25	:	17
		8

According to the question,
Note: 60% of profit should be divided equally between them

\begin{aligned} 8 units = Rs . 300 \\ 1 unit = Rs . \frac{300}{8} \\ 42 units = Rs . \frac{300 \times 42}{8} \\ 40 % of profit \\ = Rs . \frac{300 \times 42}{8} \\ 100 % profit \\ = Rs . \frac{300 \times 42 \times 100}{8 \times 40} \\ = Rs . 3937 .50 \end{aligned}

59. Two brother invested Rs. 50000 and Rs. 70000 respectively in a business and agreed that 70% of the profits should be divided equally between them and the remaining profit in the ratio of investment. If one brothers gets Rs. 90 more than the other. Find the total profit made in the business ?

A. Rs. 1200

B. Rs. 1400

C. Rs. 1600

D. Rs. 1800

Discuss

Solution:

30% of the total profit is divided in the ratio 50000 : 70000 = 5 : 7 between the two partners.
Suppose x = 30% of the total profit. Then

\begin{aligned} x \times \frac{7 - 5}{7 + 5} = 90 \\ x \times \frac{1}{6} = 90 \\ x = 540 \\ 30 % of the total profit = 540 \\ Total Profit \\ = \frac{540 \times 100}{30} \\ = 1800 \end{aligned}

Alternative
From the 30% of the profit, let first partner gets x and second partner gets (x + 90)

\begin{aligned} x : (x + 90) = 50000 : 70000 \\ x : (x + 90) = 5 : 7 \\ 7 x = 5 x + 450 \\ 2 x = 450 \\ x = 225 \\ ∴ 30 % of the profit \\ = x + x + 90 \\ = 225 + 225 + 90 \\ = 540 \\ Total Profit = \frac{540 \times 100}{30} \\ = 1800 \end{aligned}

60. A, B and C enter into a partnership. They invest Rs. 40000, Rs. 80000 and Rs. 120000 respectively. At the end of the first year, B withdraws Rs. 40000, while at the end of the second year, C withdraws Rs. 80000. In what ratio will the profit be shared at the end of 3 years ?

A. 2 : 3 : 5

B. 3 : 4 : 7

C. 4 : 5 :9

D. None of these

Discuss

Solution:

A : B : C
(40000 × 36) :(80000 × 12 + 40000 × 24) : (120000 × 24 + 40000 × 12)
= 144 : 192 : 336
= 3 : 4 : 7

1 2 3 4 5 6 7 8 9 10

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