Question

I am a fraction whose Numerator and denominator are both prime numbers less than 20. If you were to increase each term by 1‚ I would be equivalent to 1/2. What fraction am I?

Answer 1

Answer:

$\frac{2}{5}$.

Step-by-step explanation:

Let the unknown fraction be $\frac{x}{y}$  ,

where, x and y both are prime numbers less than 20.

Now, it is given that adding 1 to both numerator and denominator will make the fraction $\frac{1}{2}$.

Thus,

$\frac{x+1}{y+1}$ =  $\frac{1}{2}$

2(x + 1) = y + 1

2x + 2 = y + 1

2x + 1 = y.

Clearly if x will be any odd number , two times x will be odd and adding 1 to it will result in even number and y should be even number , which is not possible as only even prime is 2.

Thus , x should be the even prime which is 2.

And y will be 5.

Thus the required fraction is $\frac{2}{5}$.