Question

the denominator of a fraction is1 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

hope u will understand...

Answer 2

Let the numerator be x.

Denominator of a fraction = 2x + 1 .

$\bold{Increase\:both\:by\:5,}$

Numerator = x + 5.

denominator =2x + 1 + 5 = x + 6.

$\bold{According\:to\:the\:question,}$

$\implies{\dfrac{Numerator}{Denominator} = \dfrac{3}{5}}$

$\implies{\dfrac{x + 5}{2x + 6} = \dfrac{3}{5}}$

$\bold{By\:cross\:multiplication....}$

$\implies{5\times ( x + 5 ) = 3\times ( 2x + 6 )}$

$\bold{Solve\:each\:side,}$

$\implies{5x + 25 = 6x + 18}$

$\bold{Shift\:the\:terms\:and\:solve....}$

$\implies{5x - 6x = 18 - 25}$

$\implies{x = 7}$



$\therefore{\bold{x = 7}}$

$\therefore{\bold{Numerator = 7}}$

$\therefore{\bold{Denominator = 2\times 7 + 1 = 15}}$

$\therefore{Fraction =\dfrac{7}{15}}$

$\bold{The\:final\:answer\:is :}$

$\boxed{\bold{Fraction=\dfrac{7}{15}}}$