Question

the denominator of a fraction is 3 less than the nominator. increasing the numerator by 4 And decreasing the denominator by 3,we get the number 3. Find the fraction​

Answer 1

Solution :

$\underline{\bf{Given\::}}$

The denominator of a fraction is 3 less than the numerator. Increasing the numerator by 4 & decreasing the denominator by 3, we get the number is 3.

$\underline{\bf{Explanation\::}}$

Let the place of numerator be r & the denominator be (r-3) respectively;

$\therefore \boxed{\bf{The\:fraction=\frac{r}{r-3} }}$

$\underline{\boldsymbol{According\:to\:the\:question\::}}$

$\mapsto\tt{\dfrac{r+4}{(r-3)-3} =3}\\\\\\\mapsto\tt{\dfrac{r+4}{r-3-3} =3}\\\\\\\mapsto\tt{\dfrac{r+4}{r-6} =3}\\\\\\\mapsto\tt{1(r+4) = 3(r-6) \:\:\underbrace{\sf{Cross-multiplication}}}\\\\\mapsto\tt{r+4 = 3r -18}\\\\\mapsto\tt{r-3r=-18-4}\\\\\mapsto\tt{-2r = -22}\\\\\mapsto\tt{r=\cancel{-22/-2}}\\\\\mapsto\bf{r=11}$

Thus;

• Numerator = r = 11
• Denominator = r-3 = 11 - 3 = 8

$\boxed{\bf{The\:fraction=\frac{r}{r-3}=\frac{11}{11-3}=\frac{11}{8} }}$