Question

The denominator of a rational number is greater than the numerator by 6 .if the
numerator is decreased by 2 and the denominator is increased by 4, the new
rational number obtained is 1/5 Find the original number .​

Answer 1

Answer:

Step-by-step explanation:

Let the numerator of the rational number be x

So atq denominator will be x+6

Original Rational number = $\rm\dfrac{x}{x+6}$

If the numerator is decreased by 2 and the denominator is increased by 4, the new

rational number obtained is 1/5 .

Hence,

$\dashrightarrow\rm\dfrac{x-2}{x+6+4}=\dfrac{1}{5}$

$\dashrightarrow \rm \dfrac{x-2}{x+10}=\dfrac{1}{5}\\\\\dashrightarrow \rm 5(x-2)=1(x+10)\\\\\dashrightarrow \rm 5x-10=x+10\\\\\dashrightarrow \rm 5x-x=10+10\\\\\dashrightarrow \rm 4x=20\\\\\dashrightarrow \rm x=\dfrac{20}{4}\\\\\dashrightarrow \rm x=5\\\\\rm Original \ Rational \ number = \dfrac{x}{x+6} \dashrightarrow \dfrac{5}{5+6} \dashrightarrow \dfrac{5}{11}$

Hence, the original number is 5/11.