# Thread: A complex problem on number

1. ## A complex problem on number

Dear All ,

Q> When the numerator of a fraction increases by 4 ,the fraction increases by
2/3.The denominator of the fraction is ???

Ans > 6

but my doubt is in the solution:

let Fraction be - x/y.
then (x+4)/y - x/y = 2/3

ie y = 6

but why -x/y

pls explain me the solution pls

2. LHS: Numerator of the fraction increases by $\displaystyle \displaystyle 4$, so $\displaystyle \displaystyle \frac{x + 4}{y}$.

RHS: Fraction increases by $\displaystyle \displaystyle \frac{2}{3}$, so $\displaystyle \displaystyle \frac{x}{y} + \frac{2}{3}$.

Therefore

$\displaystyle \displaystyle \frac{x + 4}{y} = \frac{x}{y} + \frac{2}{3}$

$\displaystyle \displaystyle \frac{x + 4}{y} - \frac{x}{y} = \frac{2}{3}$

$\displaystyle \displaystyle \frac{x + 4 - x}{y} = \frac{2}{3}$

$\displaystyle \displaystyle \frac{4}{y} = \frac{2}{3}$.

Since $\displaystyle \displaystyle \frac{4}{6} = \frac{2}{3}$, that means $\displaystyle \displaystyle y=6$.

3. Thankx ,solution is crystal clear sir...
Thankx a lot

DexKann