Question

The numerator and the denominator of a rational number are in the ratio 7:5. When 4 is added to both the numerator and denominator, the ratio becomes 5:4. What is the rational number?

Answer 1

Answer :-

• The fraction is 28/20.

Given :-

• The numerator and the denominator of a rational number are in the ratio 7:5. When 4 is added to both the numerator and denominator, the ratio becomes 5:4.

To Find :-

• The fraction.

Solution :-

Put x in the ratio

• Numerator = 7x
• Denominator = 5x

When 4 is added

• Numerator = 7x + 4
• Denominator = 5x + 4

When 4 is added, the ratio becomes 5/4.

According to question :-

⇒ 7x + 4/5x + 4 = 5/4

⇒ 4 (7x + 4) = 5 (5x + 4)

⇒ 28x + 16 = 25x + 20

⇒ 28x - 25x = 20 - 16

⇒ 3x = 4

⇒ x = 4/3

Put the value of x in the ratio

• Numerator = 7(4/3) = 28/3
• Denominator = 5 (4/3) = 20/3

→ Fraction = (28/3)/(20/3) = 28/20

Hence, fraction = 28/20.

Answer 2

Given

• The numerator and the denominator of a rational number are in the ratio 7:5.
• When 4 is added to both the numerator and denominator, the ratio becomes 5:4.

To find

• The required fraction.

Solution

• Let the ratio be x.

$\rightarrow{\sf{Then\: the\: fraction\: will\: be\: \dfrac{7x}{5x}}}$

★ When 4 added to both tha numerator and denominator the fraction wil be

$\rightarrow{\dfrac{7x + 4}{5x + 4}}$

According to the question

⠀

$\tt:\implies{\dfrac{7x + 4}{5x + 4} = \dfrac{5}{4}}$

⠀

$\tt:\implies{4(7x + 4) = 5(5x + 4)}$

⠀

$\tt:\implies{28x + 16 = 25x + 20}$

⠀

$\tt:\implies{28x - 25x = 20 - 16}$

⠀

$\tt:\implies{3x = 4}$

⠀

$\tt:\implies{x = \dfrac{4}{3}}$

⠀

________________________

⠀

• Putting the value of x in the fraction.

⠀

$\tt:\implies{Fraction = \dfrac{7x}{5x}}$

⠀

$\tt:\implies{Fraction = \dfrac{7 × \dfrac{4}{3}}{5 × \dfrac{4}{3}}}$

⠀

$\tt:\implies{Fraction = \dfrac{\dfrac{28}{3}}{\dfrac{20}{3}}}$

⠀

$\tt:\implies{Fraction = \dfrac{\dfrac{28}{\not{3}}}{\dfrac{20}{\not{3}}}}$

⠀

$\tt:\implies{\underline{\boxed{\orange{Fraction = \dfrac{28}{20}}}}}$