Question : A, B, and C entered into a business and their investment ratio was 5 : 4 : 3. After 4 months B invested Rs. 1,000 more and after 8 months C invested Rs. 2,000 more. At the end of one year, the profit ratio was 15 : 14 : 11, then the investment of C at the beginning was:
Option 1: Rs. 3,000
Option 2: Rs. 6,000
Option 3: Rs. 4,500
Option 4: Rs. 7,500
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Correct Answer: Rs. 3,000
Solution : Let the opening shares of A, B, and C be $5x$, $4x$, and $3x$. Ratio of profit = Ratio of investment × Ratio of time The share of A, $=5x\times12=60x$ The share of B, $=4x\times12+1000\times8=48x+8000$ The share of C, $=3x\times12+2000\times4=36x+8000$ According to the question, $\frac{60x}{48x+8000}=\frac{15}{14}$ $⇒56x=48x+8000$ $⇒x=1000$ Therefore, the investment of C at the beginning = 3 × 1000 = Rs. 3,000 Hence, the correct answer is Rs. 3,000.
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