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01. Arun, Kamal and Vinay invested Rs. 8000, Rs. 4000 and Rs. 8000 respectively in a business. Arun left after six months. If after eight months, there was a gain of Rs. 4005, then what will be the share of Kamal?
A. Rs. 890 B. Rs. 1335
C. Rs. 1602 D. Rs. 1780

Answer and Explanation

Answer: Rs. 890

Explanation:
Arun : Kamal : Vinay = (8,000 x 6) : (4,000 x 8) : (8,000 x 8)
= 48 : 32 : 64
= 3 : 2 : 4.
Kamal's share = Rs. 4005 x (2/9)   = Rs. 890.

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02. A and B started a business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, C joined them with Rs. 20,000. What will be B's share in total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business? 
A. Rs. 7500 B. Rs. 9000
C. Rs. 9500 D. Rs. 10,000

Answer and Explanation

Answer: Rs. 7500

Explanation:
A : B : C = (20,000 x 24) : (15,000 x 24) : (20,000 x 18) = 4 : 3 : 3.
B's share = Rs. 25000 x (3/10)   = Rs. 7,500.

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03. A and B entered into partnership with capitals in the ratio 4 : 5. After 3 months, A withdrew 1/4  of his capital and B withdrew  1/5 of his capital. The gain at the end of 10 months was Rs. 760. A's share in this profit is: 
A. Rs. 330 B. Rs. 360
C. Rs. 380 D. Rs. 430

Answer and Explanation

Answer: Rs. 330

Explanation:

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04. A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Rs. 6500 for 6 months, B, Rs. 8400 for 5 months and C, Rs. 10,000 for 3 months. A wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Rs. 7400. Calculate the share of B in the profit. 
A. Rs. 1900 B. Rs. 2660
C. Rs. 2800 D. Rs. 2840

Answer and Explanation

Answer: Rs. 2660

Explanation:
For managing, A received = 5% of Rs. 7400 = Rs. 370.
Balance = Rs. (7400 - 370) = Rs. 7030.
Ratio of their investments = (6500 x 6) : (8400 x 5) : (10000 x 3)
= 39000 : 42000 : 30000
= 13 : 14 : 10
B's share = Rs. 7030 x (14/37)   = Rs. 2660.

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05. P, Q and R enter into a partnership. P’s share in the capital was Rs.18000. After 1 year they earn a profit of Rs.1500 of which P’s share is Rs.675 and Q’s share is 375. What was the capital invested by R? 
A. 18000  B. 10000 
C. 15000  D. 12000 

Answer and Explanation

Answer: 12000 

Explanation:
R’s share in the profit = 1500 – 675 – 375 = 450
P : Q : R = 675 : 375 : 450 = 9 : 5 : 6
Therefore, the ratio of the capital invested by P, Q, and R are in the ratio 9x : 5x : 6x
9x = 18000
x = 2000
R’s capital = 6x = 6*2000 = Rs.12000

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06. If three partners shared the profit of a business in the ratio 7 : 8 : 15 in which they had partnered for 15 months, 18 months and 6 months respectively, what was the ratio of their investments?
A. 5 : 6 : 2 B. 35 : 48 : 30
C. 168 : 160 : 900 D. 120 : 175 : 624

Answer and Explanation

Answer: 168 : 160 : 900

Explanation:

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07. Rashmi and Rakhi were partners in a business. Rashmi contributed 2/3rd of the capital for 20 months and Rakhi received 3/5th of the total profit. What was the time duration of Rakhi’s investment in the business? 
A. 45 months  B.  30 months 
C.  60 months  D. 10 months 

Answer and Explanation

Answer:  60 months 

Explanation:
Ratio of the capital = 2 : 1
Ratio of the profit = 2 : 3
Let the duration of Rakhi’s investment be x months.
(2*20) : (1*x) = 2 : 3
x = 60 months

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08. In a partnership deal, A contributes Rs 3200 for 4 months, B contributes Rs 5100 for 3 months and C contributes Rs 2700 for 5 months. How should they divide a total profit of Rs 1248 among themselves?
A. Rs 384, Rs 459, Rs 405 B. Rs 284, Rs 259, Rs 205
C. Rs 384, Rs 359, Rs 305 D. Rs 584, Rs 459, Rs 705

Answer and Explanation

Answer: Rs 384, Rs 459, Rs 405

Explanation:
We calculate the equivalent capitals for one month:
A’s capital for 1 month = Rs (3200*4) = Rs 12800
B’s capital for 1 month = Rs (5100*3) = Rs 15300
C’s capital for 1 month = Rs (2700*5) = Rs 13500

∴ the ratio of A,B and C’s share is 12800:15300: 13500 = 128:153:135
Sum of the ratios = 128 + 153 +135 = 416
A’s share = Rs (1248*128)/ 416 = Rs 384
B’s share = Rs (1248*153)/ 416 = Rs 459
C’s share = Rs (1248*135)/ 416 = Rs 405

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09. A and B entered into partnership with capitals in the ratio of 4:5. After 3 months A withdrew a/4 of his capital and B withdrew 1/5 of his capital. The gain at the end of 10 months was Rs 760, what are their shares in the profit?
A. Rs 930, Rs 530 B. Rs 130, Rs 230
C. Rs 330, Rs 430 D. Rs 330, Rs 300

Answer and Explanation

Answer: Rs 330, Rs 430

Explanation:
Let A invest Rs 4 and B invest Rs 5
A withdraws (1/4)*4 = Re. 1
A withdraws (1/5)*5 = Re. 1
Calculation the equivalent capital for 1 month:
A’s capital = Rs (4 * 3 + 3*7) = Rs 33

A’s capital = Rs (4 * 3 + 3*7) = Rs 33
B’s capital = Rs (5 * 3 + 4*7) = Rs 43
Ratio of capitals = 33:43
∴A’s share = Rs (760*33)/76 = Rs 330
B’s share = Rs (760*43)/76 = Rs 430

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10. A, B, C and D enter into a partnership. A subscribes 1/3 of the capital. B ¼, C 1/5 and D the rest. How should they divide a profit of Rs 2460?
A. Rs 820, Rs 615 , Rs 492, Rs 533 B. Rs 120, Rs 115 , Rs 192, Rs 133
C. Rs 320, Rs 315 , Rs 392, Rs 333 D. Rs 520, Rs 515 , Rs 592, Rs 533

Answer and Explanation

Answer: Rs 820, Rs 615 , Rs 492, Rs 533

Explanation:
Profit to be shared in proportion to the capital invested, periods being equal.
A,B,C,D get Rs (1/3)x, Rs(1/4)x ,Rs(1/5)x, Rs(13/60)x respectively.
(1/3)x + (1/4)x + (1/5)x +(13/60)x = 2460.
Therefore x = 2460.
A,B,C,D get Rs 820, Rs 615 , Rs 492, Rs 533 respectively

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