Question

In a fraction, twice the number is 2 more than the denominator. If 3 is added to the numerator and to the denominator, the new fraction is 2/3.Find the original fraction.​

Answer 1

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

Step-by-step explanation:

★Correct question -

• In a fraction, twice the numerator is 2 more than the denominator. If 3 is added to thenumerator and to the denominator, the new fraction is 2/3.Find the original fraction.

★Given -

• In a fraction, twice the number is 2 more than the denominator.
• If 3 is added to the numerator and to the denominator, the new fraction is 2/3.

★To find -

• The original fraction.

★Concept -

• Here, we'll use the concept of linear equations in two variables to solve the question. Let's do it!!

★Solution -

$\rm{Let \: the \: fraction \: be \: \dfrac{x}{y} }$

According to the first condition,

$\longmapsto \rm{ \bf2x = y + 2 }$

$\longmapsto \rm{ { \underline \green{\bf2x - 2= y } \: \: \: \: \: \: \: \: (1) }}$

Now, according to the second condition,

$\longmapsto \rm{ \bf\dfrac{x + 3}{y + 3 } = \dfrac{2}{3} }$

$\longmapsto \rm{ \bf (x + 3)3} \bf \: = ( y + 3)2$

$\longmapsto \rm{ \bf 3x + 9 = 2y + 6}$

${\longmapsto \rm{ \bf 3x + 9 = 2(2x - 2) + 6 \: \: \: \: \: \{from(1) \}}}$

${\longmapsto \rm{ \bf 3x + 9 = 4x - 4 + 6}}$

${\longmapsto \rm{ \bf 3x + 9 = 4x + 2}}$

${\longmapsto \rm{ \bf 9 - 2 = 4x - 3x}}$

${\longmapsto \rm{ \bf {\underline \orange{ 7 \: = \: x}}}} \: \: \: \: \: \: \: \rm \{putting \: in \: (1) \}$

$\longmapsto \rm{ \bf2(7) - 2 = y}$

$\longmapsto \rm{ \bf14- 2 = y}$

$\longmapsto \rm{ \bf \underline \pink{12 = y}}$

$\rm{ \bf{ \red{Therefore, \: the \: fraction \: is \: \dfrac{7}{12} }}}$