Question

The denominator of a fraction is 3 more than its numerator. If 2 is added to both the numerator and denominator , the new fraction is equivalent to 2/3. What is the original fraction?​

Answer 1

QUESTION:-

The denominator of a fraction is 3 more than its numerator. If 2 is added to both the numerator and denominator , the new fraction is equivalent to 2/3. What is the original fraction?

TO FIND:-

The original fraction.

SOLUTION:-

$\large{\sf{Let\:the\:original\:fraction\:be\:\dfrac{x}{y}.}}$

$\large{\underline{\underline{\bf{GIVEN\::-}}}}$

Denominator is 3 more than numerator.

Therefore,

• Let the numerator ne x.
• Denominator = x + 3.

Now it is said that,

• 2 is added to both numerator and denominator,

So,

• Numerator = x + 2
• Denominator = x + 3 + 2

According to the question,

$\large\implies{\sf{\dfrac{x+2}{x+3+2}=\dfrac{2}{3}}}$

$\large\implies{\sf{\dfrac{x+2}{x+5}=\dfrac{2}{3}}}$

By cross multiplying,

$\large\implies{\sf{3(x+2)=2(x+5)}}$

$\large\implies{\sf{3x+6=2x+10}}$

$\large\implies{\sf{3x-2x=10-6}}$

$\large\implies{\sf{x=4}}$

$\small\therefore\boxed{\sf{\blue{Numerator=x=4.}}}$

$\small\therefore\boxed{\sf{\blue{Denominator=x+3=4+3=7.}}}$

$\large{\red{\underline{\underline{\boxed{\therefore{\bf{The\:original\:fraction\:is\:\dfrac{4}{7}.}}}}}}}$