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Both the numerator and the denominator of $\dfrac{3}{4}$ are increased by a positive integer, $x,$ and those of $\dfrac{15}{17}$ are decreased by the same integer. This operation results in the same value for both the fractions.

What is the value of $x ?$

  1. $1$
  2. $2$
  3. $3$
  4. $4$
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According to the question, $\frac{3+x}{4+x} = \frac{15-x}{17-x}$

$\Rightarrow (3+x)(17-x) = (4+x)(15-x)$

$\Rightarrow \require{cancel} 51-3x + 17x – {\color{Red}{\cancel{x^{2}}}} = 60 + 15x-4x – {\color{Red}{\cancel{x^{2}}}}$

$\Rightarrow 14x-11x = 60-51$

$\Rightarrow 3x = 9$

$\Rightarrow {\color{Blue}{\boxed{x = 3}}}$

Correct Answer $:\text{C}$
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