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$A$ and $B$ start a business with initial investments in the ratio $12:11$ and their annual profits were in the ratio $4:1$. If $A$ invested the money for $11$ months, $B$ invested for:

  1. $3$ months
  2. $4$ months
  3. $\dfrac{11}{3}$ months
  4. $6$ months
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Answer is A

Let B invested money for y months.

Then, the ratio of investment   

$\frac{12x*11}{11x*y}=\frac{4}{1}$

On solving y, we will get 3 months

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