Question

a fraction becomes 1/3 when 1 is added to the numerator and becomes 1/4 when 8 is added to the deniminator. find the fraction

Answer 1

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Answer 2

$\large{\underline{\red{\rm{Correct\: Question:}}}}$

When 1 is added to the numerator the fraction becomes 1/3 and when 8 is added to the deniminatora fraction becomes 1/4. find the fraction?

$\huge{\underline{\purple{\rm{Solution:}}}}$

$\large{\underline{\red{\rm{Let:}}}}$

• $\rm{The\: numerator\:of\: fraction=N}$
• $\rm{The\: denominator\:of\: fraction=D}$
• $\rm{The\:fraction=\dfrac{N}{D}}$

$\small{\underline{\purple{\rm{As\: per\:1st\:case:}}}}$

$\rm{When\:1\:is\:added\:to\:the\:N\: fraction\: become\:1/3}$

$\rm{\implies \dfrac{N+1}{D}=\dfrac{1}{3}}$

$\rm{\implies 3N+3=D}$

$\rm{\implies 3N-D=-3}$

$\rm\green{\implies 3N-D=-3------(i)}$

$\small{\underline{\purple{\rm{As\: per\:2nd\:case:}}}}$

$\rm{When\:8\:is\:added\:to\:the\:D\: fraction\: become\:1/4}$

$\rm{\implies \dfrac{N}{D+8}=\dfrac{1}{4}}$

$\rm{\implies 4N=D+8}$

$\rm{\implies 4N-D=8}$

$\rm\green{\implies 4N-D=8-------(ii)}$

$\rm{In\:eq\:1st\: multiple\:by\:4\:and\:eq\:2\:by\:3}$

$\rm{\implies 12N-4D=-12}$

$\rm{\implies 12N-3D=24}$

• by solving equation ,we get

$\rm{\implies -D=-36}$

$\rm\red{\implies D=36}$

• Putting the value of D=36 in eq 1

$\rm{\implies 3N-D=-3}$

$\rm{\implies 3N-36=-3}$

$\rm{\implies 3N=-3+36}$

$\rm{\implies \cancel{3}N=\cancel{33}}$

$\rm\red{\implies N=11}$

Hence,

$\small{\boxed{\pink{\rm{The\: fraction=\dfrac{N}{D}=\dfrac{11}{36}}}}}$