Question

If numerator of a fraction is increased by 1 and denominator is decreased by 1 then fraction becomes 1/2. If numerator is increased by less than twice of itself while denominator is increased by 2 more than thrice of itself then fraction becomes 1/6 the original fraction is.....

Answer 1

In question ,it is not given that by how much the numerator is less ...so i assume it to be 1

Let the numeration be $x$

And denominator be $y$

$\therefore$ original fraction will be $\frac{x}{y}$

Now, According to question:

$\Rightarrow \frac{x+1}{y-1}=\frac{1}{2}$

$\Rightarrow 2x+2=y-1$

$\Rightarrow x=\frac{y-3}{2}$ ............(A)

According to condition:

$\Rightarrow \frac{x+(2x-1)}{y+(3y+2)}=\frac{1}{6}$

$\Rightarrow \frac{3x-1}{4y+2}=\frac{1}{6}$

$\Rightarrow 18x-6=4y+2$

$\Rightarrow 18x=4y+8$ ............. (B)

Put $x=\frac{y-3}{2}$ from Eq. (A) in Eq. (B), we get

$\Rightarrow 18\times \frac{y-3}{2}=4y+8$

$\Rightarrow 9y-27=4y+8$

$\Rightarrow 5y=35$

$\Rightarrow y=7$

Put $y=7$ in Eq. (B), we get

$\Rightarrow 18x=4\times 7+8$

$\Rightarrow x=2$

Hence, the original fraction is $\frac{x}{y}=\frac{2}{7}$