Question

The numerator of a fraction is 6 less than the denominator, if 3 is added to numerator fraction becomes 2/3, find original fraction

Answer 1

$\large{\underline{\underline{\red{\sf{Given: }}}}}$

• $\tt{Numerator\:of\:fraction\:is\:6\:less\:than\:denominator.}$
• $\tt{On\:adding\:3\:to\: numerator\:frac^n\:becomes\:\dfrac{2}{3}.}$

$\large{\underline{\underline{\red{\sf{To\:Find: }}}}}$

• $\tt{The\: original\:fraction.}$

$\large{\underline{\underline{\red{\sf{ Answer:}}}}}$

$\tt{Let\:us\:suppose;}$

• $\purple{\tt{Numerator\:be\:x.}}$
• $\purple{\tt{Denominator\:be\:y.}}$

$\underline{\blue{\sf{\leadsto By\:first\:given\: condition:}}}$

$\tt{\implies x + 6 = y. }$

$\tt{\implies y-x=6.}$

$\tt{\implies 2(y-x)=12.}$

$\underline{\boxed{\green{\tt{\mapsto 2y - 2x = 12.}}}}$ ................(i)

__________________________________________

$\underline{\blue{\sf{\leadsto By\:second\:given\: condition:}}}$

$\tt{\implies \dfrac{x+3}{y}=\dfrac{2}{3}.}$

$\tt{\implies 3(x+3)=2\times y.}$

$\tt{\implies 3x+9=2y.}$

$\underline{\boxed{\green{\tt{\mapsto 3x-2y =-9 .}}}}$ ...................(ii)

__________________________________________

$\underline{\pink{\sf{\leadsto Adding\:equ^n \:(i)\:and\:(ii):-:}}}$

$\tt{\implies \cancel{2y}-2x+3x\cancel{-2y}=12-9 .}$

$\tt{\implies 3x-2x = 3.}$

$\red{\tt{\underset{\blue{Value\:of\:x}}{\underbrace{\dag \:\:\:\: x \:\:\:=3\:\:\:\:}}}}$

__________________________________________

$\underline{\pink{\sf{\leadsto Putting\:this\:value\:in\:(i):}}}$

$\tt{\implies y-x=6.}$

$\tt{\implies y -3=6.}$

$\tt{\implies y=6+3 .}$

$\tt{\implies y=9.}$

$\red{\tt{\underset{\blue{Value\:of\:y}}{\underbrace{\dag \:\:\:\: y \:\:\:=9\:\:\:\:}}}}$

$\orange{\sf{\mapsto Hence\:value\:of\:x\:is\:3\:and\:y\:is\:9.}}$

$\purple{\tt{\underset{\pink{Required\:fraction.}}{\underbrace{Original\:fraction=\dfrac{x}{y}=\dfrac{3}{9}}}}}$

Answer 2

Answer:

Fraction obtained —1/3

Let the original fraction be X/y Given X=y-6, so the fraction can be written as y-6/y and

given if 3 is added to numerator then fraction becomes 2/3 so the fraction is y-6+3/y=2/3--->y-3/y=2/3---->3(y-3)=2y--->3y-2y=9--->y=9 so the fraction is y-6/y=9-6/9=3/9=1/3.