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Mathematics

Assertion (A) : The solution of : x2+x3\dfrac{x}{2} + \dfrac{x}{3} = 15 is 18.

Reason (R) : In the process of solving a linear equation, only the method of transposition is applied.

  1. Both A and R are correct, and R is the correct explanation for A.

  2. Both A and R are correct, and R is not the correct explanation for A.

  3. A is true, but R is false.

  4. A is false, but R is true.

Linear Eqns One Variable

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Answer

Given,

⇒x2+x3=15⇒3x+2x6=15⇒5x6=15⇒x=6×155⇒x=905⇒x=18\Rightarrow \dfrac{x}{2} + \dfrac{x}{3} = 15 \\[1em] \Rightarrow \dfrac{3x + 2x}{6} = 15 \\[1em] \Rightarrow \dfrac{5x}{6} = 15 \\[1em] \Rightarrow x = \dfrac{6 \times 15}{5} \\[1em] \Rightarrow x = \dfrac{90}{5} \\[1em] \Rightarrow x = 18

So, assertion (A) is true.

In the process of solving a linear equation, multiple methods can be applied, not just transposition.

So, reason (R) is false.

∴ A is true, but R is false.

Hence, option 3 is the correct option.

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