Question

The sum of the numerator and denominator
of a fraction is more than twice the numerator.
if the numerator and denominators each are
increased by 3 they are in the ratios of
2:3 determine the fraction.​

Answer 1

Answer:-

Fraction = 5/9

Step-by-step-explanation:-

★ Correct question:-

First part:- The sum of the numerator and denominator is 4 more than twice the numerator.If the numerator and denominator each of them is increased by 3,then they are in the ratio of 2: 3.What's the fraction?

★ Solution:-

Let the numerator be N and denominator be D

So,fraction = N/D

★ ATQ:-

⇒ (N + D) = 2N + 4

⇒ N - 2N = 4 - D

⇒ - N = 4 - D

⇒ - N = -(D - 4)

⇒ N = D - 4 ...............(eq.1):-

★ 2nd case:-

⇒ (N + 3) : (D + 3) = 2 : 3

⇒ (N + 3)/(D + 3) = 2/3

• Putting value from (eq.1):-

⇒ (D - 4 + 3)/(D + 3) = 2/3

⇒ (D - 1)(D + 3) = 2/3

⇒ 3D - 3 = 2D + 6

⇒ 3D - 2D = 6 + 3

⇒ D = 9

So,denominator = 9

$\rule{100}{2}$

• Putting value of D in (eq.1):-

⇒ N = 9 - 4

⇒ N = 5

So,numerator = 5.

$\rule{100}{2}$

★ Fraction:-

⇒ Fraction = N/D

⇒ Fraction = 5/9

$\therefore{\underline{\textsf{Determined\:fraction = {\textbf{ 5/9 }}}}}$

Answer 2

AnswEr :

5/9.

$\bf{\orange{\underline{\underline{\bf{Given\::}}}}}$

The sum of the numerator and denominator of a fraction is 4 more than twice the numerator. If the numerator and denominators each are increased by 3 they are in the ratio of 2:3.

$\bf{\orange{\underline{\underline{\bf{To\:find\::}}}}}$

The fraction.

$\bf{\orange{\underline{\underline{\bf{Explanation\::}}}}}$

Let the numerator be r

Let the denominator be m

$\sf{The\:fraction\:is\:\:=\red{\dfrac{r}{m} }}$

$\bigstar\bf{\purple{\underline{\underline{\tt{1_{st}\:Case\::}}}}}$

$\leadsto\sf{r+m=2r+4}\\\\\\\leadsto\sf{m=2r+4-r}\\\\\\\leadsto\sf{\red{m=r+4.......................(1)}}$

$\bigstar\bf{\purple{\underline{\underline{\tt{2_{nd}\:Case\::}}}}}$

$\leadsto\sf{(r+3):(m+3)=2:3}\\\\\\\leadsto\sf{\dfrac{r+3}{m+3} =\dfrac{2}{3} }\\\\\\\leadsto\sf{3(r+3)=2(m+3)}\\\\\\\leadsto\sf{3r+9=2m+6}\\\\\\\leadsto\sf{3r+9=2(r+4)+6\:\:\:\:\:\:\:\big[From(1)\big]}\\\\\\\leadsto\sf{3r+9=2r+8+6}\\\\\\\leadsto\sf{3r+9=2r+14}\\\\\\\leadsto\sf{3r-2r=14-9}\\\\\\\leadsto\sf{\red{r=5}}$

Putting the value of r in equation (1), we get;

$\leadsto\sf{m=5+4}\\\\\\\leadsto\sf{\red{m=9}}$

Thus,

$\underbrace{\sf{The\:fraction\:is\:=\dfrac{r}{m} =\dfrac{5}{9} }}}}$