Question

the denominator of the fraction is 1 less than twice its numerator .If 1 is added to numerator and denominator;the ration of the numberator to the denominator is 3:5 ; find the fraction please give step by step answer with statements and reason also ​

Answer 1

Fraction = 5/9

Step-by-step explanation:

Given:

• Denominator of a fraction is 1 less than twice its numerator.
• After adding 1 to numerator and denominator fraction become 3/5.

To Find:

• What is the original fraction ?

Solution: Let the numerator be x. Therefore,

Denominator = 1 less than 2x

Denominator = (2x – 1)

So the fraction will be - Numerator/Denominator

• Fraction = x/2x – 1

Now adding 1 to both

• New numerator = (x + 1)
• New denominator = (2x – 1 + 1)

A/q

• After adding 1 to numerator and denominator fraction become 3/5.

$\implies{\rm }$ (x + 1)/(2x – 1 + 1) = 3/5

$\implies{\rm }$ (x + 1)/(2x) = 3/5

$\implies{\rm }$ 5(x + 1) = 3(2x)

$\implies{\rm }$ 5x + 5 = 6x

$\implies{\rm }$ 5x – 6x = – 5

$\implies{\rm }$ – x = – 5

$\implies{\rm }$ x = 5

So the numerator is x = 5 & denominator is 2(5) – 1

= 10 – 1

= 9

Therefore original fraction is N/D = 5/9

Answer 2

□Answer□

Let the numerator be x.

So, Denominator will be 2x-1.

Now adding 1 to both denominator and numerator we get:

x+1/2x-1+1 = x+1/2x

A/Q

x+1/2x = 3/5

5x + 5 = 6x

5x - 6x = -5

x = 5

Numerator = x = 5

Denominator = 2x - 1 = 2×5 - 1 = 9

Required Fraction = 5/9