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61. 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

Discuss

Solution:

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

62. 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. 130000

Discuss

Solution:

\begin{aligned} Subhas : Aditya \\ = (25000 \times 36) : (15000 \times 6 + 30000 \times 24) \\ = 900000 : 810000 \\ = 10 : 9 \\ ∴ Aditya's share \\ \Rightarrow Rs . (247000 \times \frac{9}{19}) \\ \Rightarrow Rs .117000 \end{aligned}

63. 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

Discuss

Solution:

\begin{aligned} Here p_{1} : p_{2} : p_{3} = 5 : 3 : 12 \\ and x_{1} : x_{2} : x_{3} = 5 : 6 : 8 \\ According to the formula \\ Required ratio \\ = \frac{p_{1}}{x_{1}} : \frac{p_{2}}{x_{2}} : \frac{p_{3}}{x_{3}} \\ = \frac{5}{5} : \frac{3}{6} : \frac{12}{8} \\ = 1 : \frac{1}{2} : \frac{3}{2} \\ = 2 : 1 : 3 \\ A l t e r n a t e : \\ Profit = Time \times Capital invested \\ Time = \frac{Profit}{Capital invested} \\ Required ratio of time \\ = \frac{5}{6} : \frac{3}{6} : \frac{12}{8} \\ = 1 : \frac{1}{2} : \frac{3}{2} \\ = 2 : 1 : 3 \end{aligned}

64. 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

Discuss

Solution:

Given
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
According to the question
(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

65. 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

Discuss

Solution:

A : B : C
(5000 × 4 + 2500 × 8) : (4500 × 6 + 3000 × 6) : (7000 × 6)
= 40000 : 45000 : 42000
= 40 : 45 : 42

\begin{aligned} ∴ A's share \\ = Rs . (5080 \times \frac{40}{127}) \\ = Rs . 1600 \\ ∴ B's share \\ = Rs . (5080 \times \frac{45}{127}) \\ = Rs . 1800 \\ ∴ C's share \\ = Rs . (5080 \times \frac{42}{127}) \\ = Rs . 1680 \end{aligned}

66. 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

Discuss

Solution:

\begin{aligned} Let C = x \\ Then, B = x + 5000 and \\ A = x + 5000 + 4000 = x + 9000 \\ So, \\ \Rightarrow x + x + 5000 + x + 9000 = 50000 \\ \Rightarrow 3 x = 36000 \\ \Rightarrow x = 12000 \\ ∴ A : B : C \\ = 21000 : 17000 : 12000 \\ = 21 : 17 : 12 \\ ∴ A's share \\ = Rs . (35000 \times \frac{21}{50}) \\ = Rs. 14700 \end{aligned}

67. 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

Discuss

Solution:

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

\begin{aligned} = 337.50 : 1125 : 637.50 \\ = 9 : 30 : 17 \\ ∴ A's investment \\ = Rs . (14000 \times \frac{9}{56}) \\ = Rs. 2250 \\ B's investment \\ = Rs . (14000 \times \frac{30}{56}) \\ = Rs. 7500 \\ Hence, required difference \\ = Rs . (7500 - 2250) \\ = Rs. 5250 \end{aligned}

68. 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

Discuss

Solution:

\begin{aligned} A : B \\ 4 : 5 \\ According to the question, \\ (4 + 5) units = Rs . 14130 \\ 1 unit = \frac{14130}{9} = Rs . 1570 \\ 5 units = 5 \times 1570 = Rs . 7850 \\ ∴ Hence share of B = Rs . 7850 \end{aligned}

69. 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

Discuss

Solution:

Initial ratio of investments by A and B = 2 : 3
Let their respective investments are 2x and 3x
According to the question,
If A added Rs. 10000 to his investment
Then the new ratio = 3 : 2

\begin{aligned} \Rightarrow \frac{2 x + 10000}{3 x} = \frac{3}{2} \\ \Rightarrow 4 x + 20000 = 9 x \\ \Rightarrow 5 x = 20000 \\ \Rightarrow x = 4000 \end{aligned}

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

70. 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

Discuss

Solution:

Let the initial investments of A, B and C be Rs. 5x, Rs. 6x and Rs. 8x respectively
Then, A : B : C
[5x × 12 + (160% of 5x) × 12] : (6x × 24) : (8x × 12 + 4x × 12)
= 156x : 144x : 144x
= 13 : 12 : 12

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