Question

1. The denominator of a fraction is 3times the numerator. If 2 is
added to the numerator and 3 is
added to the denominator, then the
denominator of the new fraction
becomes 2 times the numerator.
Find
the original fraction.​

Answer 1

Step-by-step explanation:

Let the numerator be 'x'.

Therefore, denominator will be '3x'.

After adding 2,

Numerator = x+2

Denominator =3x+3

Then, denominator of new fraction will be 2x+4

x+2/3x+3 = x/2x

Therefore x=Numerator=1

Denominator= 3x=3*1=3

Therefore,

Original Fraction= 1/3.

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Answer 2

Given :-

• The denominator of a fraction is 3 times the numerator .
• If 2 is added to the numerator and 3 is added to the denominator, then the denominator of the new fraction becomes 2 times the numerator.

To find :-

• The original fraction.

Solution :-

Consider,

• Numerator = x
• Denominator = 3x

According to the question :-

• If 2 is added to the numerator and 3 is added to the denominator, then the denominator of the new fraction becomes 2 times the numerator.

$\to\sf{\dfrac{x+2}{3x+3}=\dfrac{y}{2y}}$

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

$\to\sf{3x+3=2x+4}$

$\to\sf{3x-2x=4-3}$

$\to\sf{x=1}$

• Numerator = 1
• Denominator = 3×1 = 3

Therefore,

${\boxed{\sf{Original\: fraction=\dfrac{1}{3}}}}$