Question

The denominator of a fraction is greater than it's numerator by 12. If the numerator is decrease by 2 and the denominator is increased by 7 the new fraction is equivalent with 1/2. Find the fraction

Answer 1

Solution :-

Let the numerator of the fraction be x.

Then, denominator of the fraction is x + 12.

Fraction - $\frac{x}{x+12}$

According to the question -

• If the numerator is decrease by 2

Fraction - $\frac{x-2}{x+12}$

• and the denominator is increased by 7

Fraction - $\frac{x-2}{x+12+7}=\frac{x-2}{x+19}$

• the new fraction is equivalent with 1/2 i.e.

$\frac{x-2}{x+19} = \frac{1}{2}$

Now, solving it.

=> $\frac{x-2}{x+19} = \frac{1}{2}$

=> $2(x-2)= 1(x+19)$    [Cross -multiplying it]

=> $2x-4= x+19$

=> 2x - x = 19 + 4

=> x = 23

The New Fraction -

=> $\frac{x}{x+12}$

=> $\frac{23}{23+12}$

=> $\frac{23}{35}$

Verifying the answer -

$\frac{x-2}{x+19} = \frac{1}{2}$

Here, L.H.S. = $\frac{x-2}{x+19}$

and R.H.S. = $\frac{1}{2}$

Solving L.H.S.

=> $\frac{x-2}{x+19}$

[Substituting the value of x in this fraction]

=> $\frac{23-2}{23+19}$

=> $\frac{21}{42}$

=> $\frac{1}{2}$ = R.H.S.

Therefore, the new fraction is $\frac{23}{35}$.