Question

the numerator is 2 less than denominator of a rational number. when 1 is subtracted from numerator and denominator both, then rational numberss become 1/2. find the original rational number

Answer 1

Given:

• Numerator is 2 less than denominator of a rational number.
• 1 subtracted from both numerator and denominator then rational number became 1/2

To Find:

• Original rational number ?

Solution:

Here, given that numerator of a rational is 2 less than its denominator and if 1 is subtracted from both numerator and denominator then rational number became 1/2

_____________

Let suppose that denominator of rational number is x

∴ Numerator will be x - 2

Therefore,

• Fraction will be $\small{\bf{\dfrac{x-2}{x}}}$

Now,

Given that 1 is subtracted from both numerator and denominator.

Hence,

• Fraction will become $\small{\bf{\dfrac{x-2-1}{x-1}~=~\dfrac{x-3}{x-1}}}$

According to given condition :

$\small{\bf{\dfrac{x-3}{x-1}~=~\dfrac{1}{2}}}$

[On cross multiplication]

$\implies\small{\bf{2(x-3)~=~1(x-1)}}$

$\implies\small{\bf{2x-6~=~x-1}}$

$\implies\small{\bf{2x-x~=~ -1+6}}$

$\implies\small{\bf{x~=~5}}$

Hence,

• Denominator of rational number = x = 5
• ∴ Numerator = x - 2 = 5 - 2 = 3

Therefore,

• $\small{\underline{\boxed{\red{\bf{Original~rational~number~=~\dfrac{3}{5}}}}}}$