Question

The numerator of a rationol number is less than its denominator by 4. If the numerator is multiplied by 2 and the denominator is increased by 4, the number becomes 14/15. find the number.
​

Answer 1

Given :

• Numerator of a Rational Number is less than its denominator by 4 .
• If the numerator is multiplied by 2 and the denominator is increased by 4, the number becomes 14/15.

To Find :

• The Number .

Solution :

$\longmapsto\tt{Let\:Denominator\:be=x}$

As Given that Numerator of a Rational Number is less than its denominator by 4 . So ,

$\longmapsto\tt{Numerator=x-4}$

Now ,

• If the numerator is multiplied by 2 and the denominator is increased by 4, the number becomes 14/15.

$\longmapsto\tt{Numerator=2(x-4)=2x-8}$

$\longmapsto\tt{Denominator=x+4}$

A.T.Q :

$\longmapsto\tt{\dfrac{2x-8}{x+4}=\dfrac{14}{15}}$

$\longmapsto\tt{15(2x-8)=14(x+4)}$

$\longmapsto\tt{30x-120=14x+56}$

$\longmapsto\tt{30x-14x=56+120}$

$\longmapsto\tt{16x=176}$

$\longmapsto\tt{x=\cancel\dfrac{176}{16}}$

$\longmapsto\tt\bf{x=11}$

Value of x is 11 .

Therefore :

$\longmapsto\tt{Numerator=11-4}$

$\longmapsto\tt\bf{7}$

$\longmapsto\tt\bf{Denominator=11}$

So , The Rational Number is 7/11 ..

Answer 2

Given

• The numerator of a rationol number is less than its denominator by 4.
• If the numerator is multiplied by 2 and the denominator is increased by 4, the number becomes 14/15.

To find

• The number.

Solution

• Let the denominator be x.

$\sf\pink{⟶}$ The numerator of a rationol number is less than its denominator by 4.

• Numerator = x - 4

Then,

$\sf\pink{⟶}$ If the numerator is multiplied by 2 and the denominator is increased by 4, the number becomes 14/15.

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {\dfrac{2(x - 4)}{x + 4} = \dfrac{14}{15}}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {\dfrac{2x - 8}{x + 4} = \dfrac{14}{15}}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {15(2x - 8) = 14(x + 4)}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {30x - 120 = 14x + 56}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {30x - 14x = 56 + 120}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {16x = 176}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {x = \dfrac{176}{16}}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {x = 11}$

⠀

$\sf\pink{⟶}$ $\sf\green{Required\: number = \dfrac{x - 4}{x}}$

⠀

$\sf\pink{⟶}$ $\sf\green{Required\: number = \dfrac{11 - 4}{11}}$

⠀

$\sf\pink{⟶}$ $\sf\green{Required\: number = \dfrac{7}{4}}$

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬