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

`(2)/(5)`.

Explanation:

Let the unknown fraction be
`(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
`(1)/(2)`.

Thus,

`(x+1)/(y+1)` =
`(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
`(2)/(5)`.