Question

The sum of numerator and denominator of a fraction is greater by 1
than thrice the numerator. If the numerator is decreased by 1 then the
fraction reduces to Find the fraction.​

Answer 1

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Given :-

Sum of numerator and denominator of a fraction is greater by 1

than thrice the numerator. If the numerator is decreased by 1 then the

fraction reduces to 1/3

To Find :-

Fraction

Solution :-

Let the fraction be x/y

$\sf x + y = 3(x)+1$

$\sf x + y = 3x+1$

$\sf 0-1 = 3x-x-y$

$\sf -1 = 2x -y$

$\sf y = 2x+1$

Now

When decreased by 1

$\sf\dfrac{x-1}{y} =\dfrac{1}{3}$

By cross multiplication

(y) = 3(x - 1)

y = 3x - 3

y = 3x - 3

Substituting the value of y

$\sf 3x - 2x-1=3$

$\sf x-1=3$

$\sf x =3+1$

$\sf x =4$

Finding the numerator

$\sf y = 3(4) - 3$

$\sf y = 12-3$

$\sf y =9$

$\bf Fraction = \dfrac{x}{y}$

$\sf Fraction = \dfrac{4}{9}$