A) Rs. 4200
B) Rs. 4800
C) Rs. 7200
D) Rs. 8000
Correct Answer: D
Solution :
| [d] Ratio of initial shares of A, B and C in the partnership \[A:B:C=\frac{7}{2}:\frac{4}{3}:\frac{6}{5}\] \[=\frac{7\times 15}{2\times 15}:\frac{4\times 10}{3\times 10}:\frac{6\times 6}{5\times 6}\] \[=\frac{105}{30}:\frac{40}{30}:\frac{36}{30}\] [\[\therefore \] LCM of 2, 3, 5 = 30] = 105 : 40 : 36 Let the respective shares of A, B and C be Rs. 105x, Rs. 40x and Rs. 36x. New shares of A, B and C in the partnership A = Rs. 105x for 4 months \[+\,105x\times \frac{150}{100}\] for 8 months \[=(105x\times 4)+\left( 105x\times \frac{3}{2}\times 8 \right)\] \[=420x+1260\,\,x=1680x\] B = 40x for 12 months \[=40x\times 12=480x\] C = 36x for 12 months \[=36x\times 12=432x\] A : B : C = 1680 : 480 : 432 = 35 : 10 : 9 It is a type of simple partnership, so the profit or loss of the business is distributed among the investors in the ratio of their invested money. \[\therefore \] B's share in profit \[\text{=}\frac{\text{B }\!\!'\!\!\text{ s}\,\,\text{investment}}{\text{(A+B+C) }\!\!'\!\!\text{ s}\,\,\text{investment}}\text{ }\!\!\times\!\!\text{ Total}\,\,\text{profit}\] \[\text{=}\frac{10}{35+10+9}\times 43200=\frac{10}{54}\times 43200\] \[=8000\] |
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