Question

the numerator and denominator of a rational number are in the ratio 3:4. if the denominator is increased by 3,the ratio becomes 3:5. Find the rational number​

Answer 1

Given :-

• The numerator and denominator of a rational number are in the ratio 3 : 4.
• If the denominator is increased by 3, then the ratio becomes 3 : 5

To Find :-

• The rational number.

Solution :-

Let the rational number be p/q where p is numerator and q is denominator.

According to the question,

Case 1

• Ratio of numerator and denominator is 3 : 4

⇒ p / q = 3 / 4

⇒ 4p - 3q = 0 ...(1)

Case 2

• If 3 is added to the denominator, then the ratio becomes 3 : 5

⇒ p / (q + 3) = 3 / 5

⇒ 5p = 3q + 9

⇒ 5p - 3q = 9 ...(2)

Subtracting (1) from (2) , we have

⇒ 5p - 3q - (4p - 3q) = 9 - 0

⇒ 5p - 3q - 4p + 3q = 9

⇒ p = 9

Substituting p = 9 in (1), we get

⇒ 4×9 - 3q = 0

⇒ 3q = 36

⇒ q = 12

Further,

⇒ Rational number = p / q

⇒ Rational number = 9 / 12

Hence, The required rational number is 9 / 12.

Answer 2

Step-by-step explanation:

Given

• The numerator and denominator of rational number are in the ratio 3:4

To find :

• Rational number.

Solution :

Let the ratio be x.

• Fraction = $\dfrac{3x}{4x}$

$\sf\pink{⟶}$ If the denominator is increased by 3 the ratio becomes 3: 5.

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {\dfrac{3x}{4x + 3} = \dfrac{3}{5}}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {5 × 3x = 3(4x + 3)}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {15x = 12x + 9}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {15x - 12x = 9}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {3x = 9}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {x = \dfrac{9}{3}}$

⠀

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

⠀

★ Therefore

Required fraction :

$: \implies \: \: \: \: \: \: \: \: \: \: \: \sf\dfrac{3 \times 3}{4 \times 3} \\ \\ : \implies \: \: \: \: \: \: \: \: \: \: \: \sf\dfrac{9}{12}$

the rational number is 9 / 12