Question

the denominator of a fraction is 1 more than double the numerator. On adding 2 to the numerator and subtracting 3 from the denominator , we obtain 1. Find the original fraction​

Answer 1

Solution :-

Let the numerator of a fraction be x

Denominator = 2x + 1

According to the question,

=> (x + 2)/(2x + 1 - 3) = 1

=> x + 2 = 2x - 2

=> x = 4

∴ Numerator = x = 4

Denominator = 2x + 1 = 2 × 4 + 1 = 9

Hence,

The original fraction = Numerator/Denominator = 4/9

Answer 2

Linear Equations in two variables :

Let the numerator be x and denominator be y.

Fraction becomes $\mathsf{\dfrac{x} {y}}$.

According to the question,

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

Also,

$\mathsf{\dfrac{x\:+\:2} {y\:-\:3}\:= \:1}$

( x + 2 ) = ( y - 3 )

x - y = - 3 - 2

x - ( 2x + 1) = - 5 [ From ( i ) ]

x - 2x - 1 = - 5

-x = - 5 + 1

- x = - 4

x = 4

Putting value of 'x' in value of 'y' equation ( i ),

y = 2x + 1

y = 2×4 + 1

y = 9

⛛ Fraction = $\mathsf{\dfrac{4} {9}}$.