The sum of the numerator and the denominator is 8 and their product is 15. Then the fraction is:

1. $\dfrac{5}{3}$ and $\dfrac{3}{5}$

2. $\dfrac{5}{3}$ or $\dfrac{3}{5}$

3. 3 and 5

4. 3 or 5

$\dfrac{5}{3}$ or $\dfrac{3}{5}$

Reason

It is given that the sum of the numerator and the denominator is 8.

Let the numerator of the fraction be x. So, denominator of the fraction = 8 - x

And, the product of numerator and denominator is 15.

⇒ x(8 - x) = 15

⇒ 8x - x² = 15

⇒ 8x - x² - 15 = 0

⇒ x² - 8x + 15 = 0

⇒ x² - 5x - 3x + 15 = 0

⇒ x(x - 5) - 3(x - 5) = 0

⇒ (x - 5)(x - 3) = 0

⇒ (x - 5) = 0 or (x - 3) = 0

⇒ x = 5 or x = 3

When x = 5, denominator = 8 - 5 = 3

When x = 3, denominator = 8 - 3 = 5

So, the fraction = $\dfrac{5}{3} \text{ or } \dfrac{3}{5}$.

Hence, option 2 is the correct option.