Question

the denominator of a fraction is one more than twice its numerator. if the numerator and denominator are both increased by 5, it becomes 3/5. find the original fraction ​

Answer 1

Answer:

Let the numerator be x. Then it's denominator is 2x-1

If the numerator and the denominator both increased by 1 the fraction becomes 3/5.

So (x+1)/(2x-1+1) = 3/5

ie (x+1)/2x = 3/5 => 6x = 5x + 5 => x = 5

So the numerator is 5 and hence the denominator is 2×5 - 1= 9

So the fraction is 5/9

Answer 2

S O L U T I O N :

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

The denominator of a fraction is one more than twice it's numerator. If the numerator & denominator are both increased by 5, it becomes 3/5 .

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

Let the numerator place be r & the denominator place be 2r + 1 .

$\boxed{\bf{The\:original\:fraction = \frac{r}{2r+1} }}$

$\underline{\underline{\tt{According\:to\:the\:question\::}}}$

$\mapsto\rm{\dfrac{r+5}{2r+1+5} = \dfrac{3}{5}}$

$\mapsto\rm{\dfrac{r+5}{2r+6} = \dfrac{3}{5}}$

$\mapsto\rm{5(r+5) = 3(2r + 6) \:\:\: \underbrace{\sf{cross-multiplication}}}$

$\mapsto\rm{5r + 25 = 6r + 18}$

$\mapsto\rm{5r -6r = 18-25}$

$\mapsto\rm{\cancel{-}r =\cancel{ -}7}$

$\mapsto\bf{r=7}$

Thus;

• Numerator = r = 7
• Denominator = 2r + 1 = 2(7) + 1 = 14 + 1 = 15

$\boxed{\bf{The\:original\:fraction = \frac{r}{2r+1} = \frac{7}{2(7) + 1} = \frac{7}{15} }}$