Question

please tell 13 wala
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Answer 1

$\textsf{Let the Rational Number be : R}$

$\mathsf{Given : This\;Rational\;Number\;is\;multiplied\;by\;\dfrac{5}{2}}$

$\mathsf{The\;Resulting\;Number\;will\;be : \bigg(\dfrac{5}{2} \times R\bigg) = \dfrac{5R}{2}}$

$\mathsf{Given : \dfrac{2}{3}\;is\;added\;to\;the\;Resulting\;Product}$

$\mathsf{\implies \bigg(\dfrac{5R}{2} + \dfrac{2}{3}\bigg)}$

$\mathsf{Given : After\;adding\;\dfrac{2}{3},\;We\;get\;the\;Number\;\dfrac{7}{12}\;as\;Result}$

$\mathsf{\implies \bigg(\dfrac{5R}{2} + \dfrac{2}{3}\bigg) = \dfrac{7}{12}}$

$\mathsf{\implies \bigg[\dfrac{3(5R) + 2(2)}{6} \bigg] = \dfrac{7}{12}}$

$\mathsf{\implies \bigg[\dfrac{15R + 4}{6} \bigg] = \dfrac{7}{12}}$

$\mathsf{\implies 12(15R + 4) = 6\times 7}$

$\mathsf{\implies 180R + 48 = 42}$

$\mathsf{\implies 180R = 42 - 48}$

$\mathsf{\implies 180R = -6}$

$\mathsf{\implies R = \dfrac{-6}{180}}$

$\mathsf{\implies R = \dfrac{-1}{30}}$

$\underline{\bf{Answer}} : \mathsf{The\;Rational\;Number\;is : \dfrac{-1}{30}}$