Math, asked by tiwarirakesh64, 3 months ago

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.​

Answers

Answered by abhi569
52

Seems like the question contains "fraction reduces to 1/3

Answer:

4/9

Step-by-step explanation:

Let the numerator be 'x' and denominator be 'y'. Thus, fraction be x/y.

Sum of x and y = 1 + 3x

            x + y = 1 + 3x

                  y = 1 + 2x  

If the numerator is decreased by 1, fraction becomes 1/3.

⇒ (x - 1)/y = 1/3

⇒ (x - 1)/(1 + 2x) = 1/3

⇒ 3(x - 1) = 1 + 2x

⇒ 3x - 3 = 1 + 2x

⇒ 3x - 2x = 4       ⇒ x = 4

  thus, y = 1 + 2x = 1 + 2(4) = 9

∴ Fraction = x/y = 4/9

Answered by Anonymous
63

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}

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