Question

The numerator of a fraction is 4 less then it's denominator. If the numerator us decreased by 1,the fraction becomes 2 by 3,Find the fraction.​

Answer 1

$\large\underline{\sf{Solution-}}$

Let numerator be x

Let denominator be y

So,

$\rm :\longmapsto\:Fraction = \dfrac{x}{y}$

Now,

According to statement,

Numerator of a fraction is 4 less then it's denominator.

$\rm :\longmapsto\:x = y - 4 - - - (1)$

According to statement again,

If the numerator is decreased by 1, the fraction becomes 2 by 3.

Now,

Numerator = x - 1

Denominator = y

So,

$\rm :\longmapsto\:Fraction = \dfrac{x - 1}{y}$

According to given,

$\rm :\longmapsto\: \dfrac{x - 1}{y} = \dfrac{2}{3}$

$\rm :\longmapsto\: \dfrac{y - 4 - 1}{y} = \dfrac{2}{3}$

$\rm :\longmapsto\: \dfrac{y - 5}{y} = \dfrac{2}{3}$

$\rm :\longmapsto\:3y - 15 = 2y$

$\rm :\longmapsto\:3y - 2y = 15$

$\rm :\longmapsto\:y = 15$

On substituting the value of y in equation (1), we get

$\rm :\longmapsto\:x = 15 - 4$

$\rm :\longmapsto\:x = 11$

Hence,

Numerator, x = 11

Denominator, y = 15

$\rm :\longmapsto\:Fraction = \dfrac{x}{y} = \dfrac{11}{15}$

Verification :-

Numerator = 11

Denominator = 15

So, it implies numerator of a fraction is 4 less then it's denominator.

Hence, first condition verified.

Now,

If the numerator is decreased by 1,the fraction becomes 2 by 3.

$\rm :\longmapsto\:\dfrac{11 - 1}{15} = \dfrac{10}{15} = \dfrac{2}{3}$

Hence, second condition verified.