Question

the denominator of fraction is 6 more than its numerator of the denominator is increased by 5and the numerator is decreased by 1 the fraction becomes 2/3 find the fraction​

Answer 1

Answer:

The fraction is     $\frac{25}{31}$

Step-by-step explanation:

Let the numerator be n and the denominator be n+6

then the fraction will be,

⇒ $\frac{n}{n+6}$

Now, according to the situation, the denominator is increased by 5 and the numerator is decreased by 1 to become 2/3.

So, the fraction will now become,

⇒ $\frac{n-1}{n+11} = \frac{2}{3}$

Now, by cross multiplying the equation, we get

⇒ $3(n-1) = 2(n+11)$

⇒ $3n-3 = 2n+22$

Now, equating both the sides,

⇒ $3n - 2n = 22+3$

⇒ $n = 25$

∴ the numerator is n = 25 and

the denominator is n+6 = 31

Verification:-

⇒  $\frac{25-(1)}{31+5}$                              (as per the given situation)

⇒ $\frac{24}{36} = \frac{2}{3}$

Hence, the answer is correct.