1.

The numerator of a fraction is six less than thedenominator. If three is added to the numerator, the fraction becomes 2/3. Find the original fraction.​

Answer»

❍ Let the DENOMINATOR be x and according to the GIVEN question, the numerator be (x - 6) respectively.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

━ Therefore, the fraction will be,

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

:\implies\sf{\dfrac{x-6}{x}}\qquad\qquad\bigg\lgroup\sf{eq^n\;1}\bigg\rgroup

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

\underline{\bigstar\;\boldsymbol{According\;to\;the\;Question:}}

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

  • When three is ADDED to the numerator, then the fraction BECOMES 2/3.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Therefore,

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

:\implies\sf{\dfrac{x-6+3}{x}=\dfrac{2}{3}}\\\\\\\\:\implies\sf{\dfrac{x-3}{x}=\dfrac{2}{3}}

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

\qquad\qquad\underline{\footnotesize{\bf{\dag}\frak{\;Cross\;multiplying:}}}

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

:\implies\sf{3x-9=2x}\\\\\\\\:\implies\sf{3x-2x=2x}\\\\\\\\:\implies\underline{\boxed{\pink{\frak{x=9}}}}{\;\bigstar}

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

\qquad\qquad\underline{\footnotesize{\bf{\dag}\frak{\;Putting\;value\;of\;x\;in\;eq^n\;1:}}}

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

:\implies\sf{\dfrac{x-6}{x}}\\\\\\\\:\implies\sf{\dfrac{9-6}{9}}\\\\\\\\:\implies\sf{\cancel{\dfrac{3}{9}}}\\\\\\\\:\implies\underline{\boxed{\purple{\frak{\dfrac{1}{3}}}}}{\;\bigstar}

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

\therefore\;{\underline{\sf{Hence,\;the\;original\;fraction\;is\;{\frak{\dfrac{1}{3}}}}.}}⠀⠀


Discussion

No Comment Found

Related InterviewSolutions