Question

solve this question ​

Answer 1

Given

• The denominator of a fraction is 1 less than twice it's numerator
• If 1 is added to the numerator and denominator, the ratio of numerator and denominator is 3:5

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To Find

• The fraction

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Solution

Let the numerator be 'x'.

Denominator would be ⇒ 2x - 1

After adding 1 to the numerator and denominator,

Numerator ⇒ x + 1

Denominator ⇒ 2x - 1 + 1

According to the question when we add '1' to the numerator and denominator the ratio of the numerator and denominator is 3:5. So the equation we'll solve to find the fraction is ⇒ $\dfrac{x+1}{2x-1+1} = \dfrac{3}{5}$

Let's solve your equation step-by-step.

$\dfrac{x+1}{2x-1+1} = \dfrac{3}{5}$

Step 1: Simplify the equation.

⇒ $\dfrac{x+1}{2x-1+1} = \dfrac{3}{5}$

⇒ $\dfrac{x+1}{2x} = \dfrac{3}{5}$

Step 2: Cross multiply.

⇒ $\dfrac{x+1}{2x} = \dfrac{3}{5}$

⇒ $3(2x) = 5(x+1)$

⇒ $6x = 5x+5$

Step 3: Subtract '5x' from both sides of the equation.

⇒ $6x - 5x = 5x - 5x +5$

⇒ $x = 5$

∴ x = 5

∴ Numerator ⇒ x ⇒ 5

∴ Denominator ⇒ 2x - 1 ⇒ 2(5) - 1 ⇒ 10 - 1  ⇒ 9

∴ The fraction is ⇒ $\bf \dfrac{5}{9}$

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Answer 2

${\large{\bold{\rm{\underline{Question}}}}}$

✠ The denominator of a fraction is 1 less than twice it's a numerator. If 1 is added to the numerator and denominator, the ratio of numerator and denominator is 3:5 find the fraction.

${\large{\bold{\rm{\underline{Given \; that}}}}}$

✠ The denominator of a fraction is 1 less than twice it's a numerator.

✠ 1 is added to the numerator and denominator

✠ The ratio of numerator and denominator is 3:5

${\large{\bold{\rm{\underline{To \; find}}}}}$

✠ The fraction (atq..!)

${\large{\bold{\rm{\underline{Solution}}}}}$

✠ The denominator of a fraction is 1 less than twice it's a numerator. If 1 is added to the numerator and denominator, the ratio of numerator and denominator is 3:5. The fraction is ${\bf{\dfrac{5}{9}}}$

${\large{\bold{\rm{\underline{Assumptions}}}}}$

✰ Let x is numerator

✰ Let y is denominator

${\large{\bold{\rm{\underline{Full \; Solution}}}}}$

~ As it's already given that the the denominator of a fraction is 1 less than twice it's a numerator. Henceforth, the formed equation is ⬇️

${\rm{:\implies y \: = 2x - 1}}$ ①Eq.

~ It is also given that, 1 is added to the numerator and denominator, the ratio of numerator and denominator is 3:5. Henceforth, the formed data is ⬇️

${\rm{:\implies x+1 \: : 2x-1+1 \: = 3:5}}$

• - and + cancel each other..!

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

• Writing in fraction..!

${\rm{:\implies \dfrac{x+1}{2x} \: = \dfrac{3}{5}}}$

• Cross multiply them.

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

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

• Combining like terms..!

${\rm{:\implies 5 \: = 6x-5x}}$

${\rm{:\implies 5 \: = 1x}}$

${\rm{:\implies 5 \: = x}}$

${\rm{:\implies x \: = 5}}$

$\dag{\underline{\frak{Henceforth, \: x \: or \: numerator \: is \: 5}}}$

~ Now let's imply the value of x as 5 in the already formed equation ⬇️

${\rm{:\implies y \: = 2x-1}}$

${\rm{:\implies y \: = 2(5)-1}}$

${\rm{:\implies y \: = 10-1}}$

${\rm{:\implies y \: = 9}}$

$\dag{\underline{\frak{Henceforth, \: y \: or \: denominator \: is \: 9}}}$

~ That's why the formed fraction be ⬇️

${\rm{:\implies \dfrac{x}{y} \: = \: \dfrac{5}{9}}}$