Question

the denominator of a fraction is 2less then twice the numerator. if 3 is added to numerator and denominator both the new fraction is 2/3.find the original fraction.
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Answer 1

Let the numerator be x..

Now ATQ,

The denominator of the fraction is 2 less than twice the numerator

Twice the numerator = 2x

And 2 less from twice the numerator = 2x - 2.

Hence,

Denominator = 2x - 2

And original fraction = $\rm \dfrac{x}{2x-2}$

Now ATQ,

If 3 is added to numerator and denominator both the new fraction is 2/3.

Hence,

$\dashrightarrow\rm\dfrac{x+3}{2x-2+3} = \dfrac{2}{3}$

$\dashrightarrow\rm\dfrac{x+3}{2x+1} = \dfrac{2}{3}$

$\dashrightarrow\rm 3(x + 3) = 2(2x + 1)$

$\dashrightarrow\rm 3x + 9 = 4x + 2$

$\dashrightarrow\rm 9 - 2 = 4x - 3x$

$\dashrightarrow\rm 7= x$

Original fraction = $\rm \dfrac{x}{2x-2}$

$\rm \dashrightarrow \dfrac{7}{2(7)-2}$

$\rm \dashrightarrow \dfrac{7}{14-2}$

$\rm \dashrightarrow \dfrac{7}{12}$

Hence, the original fraction is 7/12.