Question

15.The denominator of a rational number is greater than its numerator by 6.if the numerator is increased by 5 and the denominator is decreased by 3, the number becomes 5/4. Find the rational number​

Answer 1

Answer :-

Given :-

• Denominator is 6 more than numerator.

• When the numerator is increased by 5 and the denominator is decreased by 3, the new fraction becomes 5/4.

To Find :-

• Fraction

Solution :-

Let the numerator be x

Denominator = x + 6

Numerator is increased by 5 -

New numerator = x + 5

Denominator is decreased by 3 :-

New denominator = x + 6 - 3 = x + 3

According to the question :-

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

$\implies\sf 4(x + 5) = 5 ( x+3)$

$\implies\sf 4x + 20 = 5x + 15$

$\implies\sf 5x - 4x = 20 - 15$

$\implies\sf x = 5$

• Numerator = 5
• Denominator = 5 + 6 = 11

$\implies\boxed{\bf Fraction = \dfrac{5}{11}}$

Answer 2

Given,

• The denominator of a rational number is greater than its numerator by 6.
• If the numerator is increased by 5 and the denominator is decreased by 3.
• The number becomes 5/4.

To Find,

• The Rational Number.

Solution,

Let's,

The Numerator = X

So,

The Denominator = X + 6

Therefore,

The Rational Number = X/(X + 6)

After Increasing numerator by 5 and decreasing denominator by 3,

The Numerator = X + 5

The Denominator = X + 6 - 3

The Denominator = X + 3

Therefore,

The New Rational Number = (X + 5)/(X + 3)

According to Question,

The New Rational Number = 5/4

→ (X + 5)/(X + 3) = 5/4

→ 4 × (X + 5) = 5 × (X + 3)

→ 4X + 20 = 5X + 15

→ 20 - 15 = 5X - 4X

→ X = 5

Required Answer,

The Rational Number = X/(X + 6)

→ The Rational Number = 5/(5 + 6)

→ The Rational Number = 5/11