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

Answer :-

• The fraction is 9/12.

Given :-

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

To Find :-

• Rational number.

Solution :-

Put x in the ratio

• Numerator = 3x
• Denominator = 4x

→ Denominator is increased by 3 = 4x + 3

Then, ratio becomes 3 : 5

According to question :-

⇒3x/(4x + 3) = 3/5

⇒3x × 5 = 3 (4x + 3)

⇒5x = 12x + 9

⇒15x - 12x = 9

⇒ 3x = 9

⇒ x = 9/3

⇒ x = 3

Put the value of x in the ratio

• Numerator = 3x = 3 × 3 = 9
• Denominator = 4x = 4 × 3 = 12

Hence, the fraction is 9/12.

Answer 2

Given

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

To find

• The rational number.

Solution

• Let the ratio be x.

» Fraction = $\dfrac{3x}{4x}$

★ Denominator increased by 3, the ratio becomes 3:5.

→ $\dfrac{3x}{4x + 3}$ = $\dfrac{3}{5}$

→ 3x × 5 = 3 × (4x + 3)

→ 15x = 12x + 9

→ 15x - 12x = 9

→ 3x = 9

→ x = 3

Hence,

• Fraction = $\dfrac{3x}{4x}$

• Fraction = $\dfrac{3 × 3}{4 × 3}$

• Fraction = $\dfrac{9}{12}$