A, B and C invested money in the ratio of $$\frac{1}{2}:\frac{1}{3}:\frac{1}{5}$$ in a business. After 4 months A doubled his investment and after 6 months B halves his investment. If the total profit at the end of the year be Rs. 34650 then find the share of each in profit ?
A. Rs. 20000, Rs. 25000, Rs. 18000
B. Rs. 15500, Rs. 27200, Rs. 20450
C. Rs. 22500, Rs. 6750, Rs. 5400
D. Rs. 10350, Rs. 21540, Rs. 12050
Answer: Option C
Solution(By Examveda Team)
Ratio of capital invested by$${\text{A, B and C}} = 15:10:6$$
Total capital invested by A in 1 year
$$\eqalign{ & = 15x \times 4 + 30x \times 8 \cr & = 300x \cr} $$
Total capital invested by B in 1 year
$$\eqalign{ & = 10x \times 6 + 5x \times 6 \cr & = 90x \cr} $$
Total capital invested by C in 1 year
$$\eqalign{ & = 6x \times 12 \cr & = 72x \cr} $$
Ratio of profits:
A | : | B | : | C |
300x | : | 90x | : | 72x |
50x | : | 15x | : | 12x |
According to the question,
$$ \Leftrightarrow \left( {50x + 15x + 12x} \right)$$ = $${\text{Rs}}{\text{. 34650}}$$
$$\eqalign{ & \Leftrightarrow 77x = {\text{Rs}}.{\text{ }}34650 \cr & \Leftrightarrow x = {\text{Rs}}{\text{. }}\frac{{34650}}{{77}} \cr & \Leftrightarrow x = {\text{Rs}}{\text{. }}450 \cr & {\text{Profit of A}} = {\text{Rs}}{\text{. }}450 \times 50 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. 22500}} \cr & {\text{Profit of B}} = {\text{Rs}}{\text{. }}450 \times 15 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. 6750}} \cr & {\text{Profit of C}} = {\text{Rs}}{\text{. }}450 \times 12 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. 5400}} \cr} $$
Related Questions on Partnership
A. 5 : 7 : 8
B. 20 : 49 : 64
C. 38 : 28 : 21
D. None of these
A. Rs. 40000
B. Rs. 50000
C. Rs. 60000
D. Rs. 70000
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