Question

the denominator of rational no is greater than its numerator by 7. if the mumerator is increased by 17 and the deniminator decreased by 6 ,the new no becomes 2. find the original number​

Answer 1

Let the numerator be 'x'

Thus, denominator = (x + 7)

Thus, fraction = x/(x+7)

According to the question,

New Numerator = x + 17

New denominator = x + 7 - 6 = x + 1

New Fraction = 2

=> (x+17)/(x+1) = 2

On cross-multiplying we get,

x + 17 = 2(x+1)

=> x + 17 = 2x + 2

=> 2x - x = 17 - 2

=> x = 15

Thus original numerator = 15 and

original denominator = 15 + 7 = 22

Thus, original fraction = 15/22

Answer 2

Let the numerator of the rational number be x.

then denominator will be x+7

Then the fraction will become $\rm \dfrac{x}{x+7}$

As per the Question, if numerator is increased by 17, and denominator is decreased 6, the number becomes 2..

Therefore,

$\sf\implies \dfrac{x+17}{x+7-6}=2$

$\sf\implies\dfrac{x+17}{x+1}=2$

$\sf\implies x+17=2(x+1)$

$\sf\implies x+17=2x+2$

$\sf\implies 17-2=2x-x$

$\sf\implies 15=x$

Therefore, the original number is

$\sf \dfrac{x}{x+7}\implies\dfrac{15}{15+7} = \dfrac{15}{22}$

Hope it helps.