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.


Good Morning everyone ​

Answer 1

Linear Equations in two variables :

Let the numerator be x and denominator be y.

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

y

x

.

According to the question,

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

Also,

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

y−3

x+2

=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}}

4/9

Good Morning Ji......☺☺✌

❤Sweetheart❤

$...$

Answer 2

Answer:

Fraction = 4/9

Step-by-step explanation:

Given:

• 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

To Find:

• The original fraction

Solution:

Let the numerator of the fraction be x.

Hence by given,

Denominator = 1 + 2 (numerator)

Denominator = 1 + 2x

Hence,

$\sf The\:fraction = \dfrac{x}{2x+1}$

Also by given, adding 2 to the numerator and subtracting 3 from the denominator, we obtain 1.

Therefore,

$\sf \dfrac{x+2}{2x+1-3} =\dfrac{1}{1}$

$\sf \dfrac{x+2}{2x-2} =\dfrac{1}{1}$

Cross multiplying we get,

2x - 2 = x + 2

2x - x = 2 + 2

x = 4

Hence the numerator of the fraction is 4.

Now finding the denominator,

Denominator = 2x + 1

Denominator = 2 × 4 + 1 = 9

Therefore denominator is 9.

Hence the fraction is 4/9.