Question

A fraction becomes 1/3 when 1 is subtracted from its numerator and it becomes 1/4 when 8 is added to its denominator. Find the fraction

Answer 1

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Answer 2

The fraction is $\dfrac{5}{12}$.

Step-by-step explanation:

let the fraction is $\dfrac{x}{y}$.

According to the given condition,

A fraction becomes 1/3 when 1 is subtracted from its numerator. So,

$\dfrac{x-1}{y}=\dfrac{1}{3}\\\\3x-3=y\\\\3x-y=3\ .....(1)$

The fraction becomes 1/4 when 8 is added to its denominator. So,

$\dfrac{x}{y+8}=\dfrac{1}{4}\\\\4x=y+8\\\\4x-y=8\ .....(2)$

Solving equation (1) and (2) we get :

$x=5$

Put x = 5 in equation (1) :

$3(5)-y=3\\\\y=12$

So, the fraction is $\dfrac{5}{12}$.

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Fraction

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