Question

Numerator of a fraction is 2 less than the Denominator. If 1 is added to the Numerator and 3 to the Denominator then the fraction becomes 2/3.Find the original fraction.​

Answer 1

$\large\bf\underline {To \: find:-}$

• we need to find the original fraction.

$\huge\bf\underline{Solution:-}$

$\bf\underline{\red{Given:-}}$

• Numerator of fraction is 2 less than the denominator.

• If 1 is added to the Numerator and 3 to the Denominator then the fraction becomes 2/3.

Let the numerator be x and denominator be y

So, the fraction is x/y

• ⚘ According to Question :-

If 1 is added to the Numerator and 3 to the Denominator then the fraction becomes 2/3.

↝ x + 1/y + 3 = 2/3

↝ 3(x + 1) = 2( y + 3)

↝ 3x + 3 = 2y + 6

↝ 3x - 2y = 3 ....2)

As we know that, Numerator of fraction is 2 less then the denominator

then, Numerator x = y - 2 .....2)

• putting value of x in 1)

↠ 3( y - 2) - 2y = 3

↠ 3y - 6 - 2y = 3

↠ y = 3 + 6

↠ y = 9

• putting value of y in 2)

⇝ x = y - 2

⇝ x = 9 -2

⇝ x = 7

So,

• The original fraction x/y = 7/9

━━━━━━━━━━━━━━━━━━━━━━━━━

Answer 2

$\huge \bf \underline\blue{Given}$

Numerator of fraction is 2 less than the denominator.

If 1 is added to the Numerator and 3 to the Denominator then the fraction becomes 2/3.

Let the numerator be x and denominator be y

So, the fraction is x/y

$\huge\underline{ \underline{ \mathbb{ { \green{ So{ \pink{Lu{ \red{TI{ \purple{ON \: }}}}} }}}}}}$

⚘ According to Question :-

If 1 is added to the Numerator and 3 to the Denominator then the fraction becomes 2/3.

↝ x + 1/y + 3 = 2/3

↝ 3(x + 1) = 2( y + 3)

↝ 3x + 3 = 2y + 6

↝ 3x - 2y = 3 ....2)

As we know that, Numerator of fraction is 2 less then the denominator

then, Numerator x = y - 2 .....2)

putting value of x in 1)

↠ 3( y - 2) - 2y = 3

↠ 3y - 6 - 2y = 3

↠ y = 3 + 6

↠ y = 9

putting value of y in 2)

⇝ x = y - 2

⇝ x = 9 -2

⇝ x = 7

So,

The original fraction x/y = 7/9

━━━━━━━━━━━━━━━━━━━━━━━━━