Question

4. If three is subtracted from the numerator and five is
added to the denominator of a fraction, the new frac-
tion formed is 1/2. If two is added to the numerator
of the initial fraction, the ratio of the new numerator
to the denominator becomes 1 : 1. Find the original
fraction.
(A) 11/13
(B) 18/23
(C) 13/15
(D) 13/11​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

Original fraction is $\frac{13}{15}$

Step-by-step explanation:

Let the fraction be $\frac{x}{y}$

Where x is numerator and y is denominator.

Given, 3 is subtracted from the numerator and five is

added to the denominator of a fraction.

So, the fraction becomes $\frac{x - 3}{y + 5}$

It is also given,the fraction now is equal to $\frac{1}{2}$

According to question,

$\frac{x - 3}{y + 5} = \frac{1}{2} \\ 2x - 6 = y + 5 \\ 2x - y - 6 - 5 = 0 \\ 2x - y - 11 = 0......(1)$

Again given,If two is added to the numerator

of the initial fraction.

So,now numerator of the initial fraction

$= (x + 2)$

It is also given ratio of the new numerator

to the denominator becomes 1 : 1.

According to question,

$(x + 2) \ratio \: y = 1 \ratio 1 \\ \frac{x + 2}{y} = \frac{1}{1} \\ x + 2 = y \\ x - y + 2 = 0....(2)$

We are Subtracting equation (1) from equation (2),

$(x - y + 2) - (2x - y - 11) = 0 \\ x - y + 2 - 2x + y + 11 = 0 \\ - x + 13 = 0 \\ x = 13$

We are putting x = 13 in equation (2),

$13 - y + 2 = 0 \\ - y = - 13 - 2 \\ y = 15$

Required fraction is $\frac{13}{15}$

Know more about about fraction,

1.https://brainly.in/question/9833636

2.https://brainly.in/question/16383044

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