Question

the denominator of a rational number is 4 less than twice the numerator. if the numerator is increased by 5 an the denominator is decreased by 6, the number obtained is 3/5. fine the rational numbers​

Answer 1

Answer:

$let \: the \: numerator \: be \: x \\ initially = \frac{x}{2x - 4} \\ finally = \frac{ x + 5}{2x - 4 - 6} = \frac{3}{5} \\ = \frac{x + 5}{2x - 10} = \frac{3}{5} \\ = 5(x + 5) = 3(2x - 10) \\ = 5x + 25 = 6x - 30 \\ 5x - 6x = - 30 - 25 \\ - x = - 55 \\ x = 55$

Step-by-step explanation:

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Answer 2

Given:

• Denominator of a rational number is 4 less than twice the numerator.
• Numerator is increased by 5 an the denominator is decreased by 6, then obtained number is 3/5

To Find:

• Rational number?

Solution:

As per given that denominator of a rational number is 4 less than twice the numerator,

☆ Let suppose that Numerator is x

☆ ∴ Denominator of rational number will be 2x - 4

Fraction will be :

• $\large{\bf{\dfrac{x}{2x-4}}}$

Now,

Given that numerator increased by 5 and denominator decreased by 6 that given 3/5.

Therefore,

According to given condition :

$\small{\bf{\dfrac{x+5}{2x-4-6}}} ~ = ~ \dfrac{3}{5}$

$\implies\small{\bf{\dfrac{x+5}{2x-10}~ = ~ \dfrac{3}{5}}}$

[On cross multiplication]

$\implies\small{\bf{5(x+5)~ = ~ 3(2x-10)}}$

$\implies\small{\bf{5x + 25 ~ = ~ 6x - 30}}$

$\implies\small{\bf{5x-6x ~ = ~ -30-25}}$

$\implies\small{\bf{ -x ~=~-55}}$

[ sign of -ve is in both so both will be cancelled]

$\implies\small{\bf{x~=~55}}$

Therefore,

• Numerator of rational number = 55
• Denominator of rational number = 55×2 - 4 = 110 - 4 = 106

Required rational number is :

• $\large{\underline{\boxed{\bf{\red{Rational~number~is~\dfrac{55}{106}}}}}}$