Question

please solve it fast and also give steps

Answer 1

$let \: fraction \: be \: \frac{x}{y} \\ so \: according \: to \: given \: situation \\ \frac{x}{y + 1} = \frac{1}{2} \\ 2x = y + 1 \\ y = 2x - 1.. - - - (1) \\ \: other\: situation \\ \frac{x + 1}{y} = 1 \\ x = y - 1.. - - - (2) \\ put \: value \: of \: x \: in \: eq.1 \\ so \: w \: gt \\ y = 2(y - 1) - 1 \\ y = 2y - 2 - 1 \\ y = 3. \\ put \: value \: of \: y \: in \: eq.2 \\ so \\ x = 3 - 1 \\ x = 2$
$fraction \: will \: be \: \frac{2}{3}$

Answer 2

Let the numerator be x and the denominator be y.

The original fraction = (x/y)

Given that if 1 is added to the denominator of a fraction, it becomes (1/2).

= > (x)/(y + 1) = (1/2)

= > 2x = y + 1

= > 2x - y = 1 ------ (1)

Given that if 1 is added to the numerator, it becomes 1.

= > (x + 1)/y = 1

= > x - y = -1 ----- (2)

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On solving (1) & (2) * 2, we get

= > 2x - y = 1

= > 2x - 2y = -2

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y = 3

Substitute y = 3 in (1), we get

= > 2x - y = 1

= > 2x - 3 = 1

= > 2x = 4

= > x = 2.

Therefore, the original fraction = (2/3).

Hope this helps!