Question

Denominator of a rational number exceeds its numerator by 8. If 7 is added to its numerator
and denominator, then the number becomes
3
4
. Find the rational number.

Answer 1

Given :- Denominator of a rational number exceeds its numerator by 8. If 7 is added to its numerator and denominator, then the number becomes 3/4 . Find the rational number. ?

Solution :-

Let us assume that, the numerator of rational number is x .

so,

→ Denominator = (x + 8) .

now,

→ (Numerator + 7) / (Denominator + 7) = 3/4

→ (x + 7)/(x + 8 + 7) = 3/4

→ 4(x + 7) = 3(x + 15)

→ 4x + 28 = 3x + 45

→ 4x - 3x = 45 - 28

→ x = 17 .

then,

→ Denominator = (x + 8) = (17 + 8) = 25 .

therefore,

→ Required Rational number = 17/25 (Ans.)

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Answer 2

Given:

The denominator of a rational number exceeds its numerator by 8. If 7 is added to its numerator and denominator, becomes 3/4.

To find:

Find the rational number.

Solution:

The denominator of a rational number exceeds its numerator by 8.

Let the numerator is x

The denominator = x+8

If 7 is added to its numerator and denominator, then the number becomes 3/4.

$= > \dfrac{x + 7}{x + 8 + 7} = \dfrac{3}{4}$

$= > \dfrac{x + 7}{x + 15} = \dfrac{3}{4}$

$= > 4(x + 7) = 3(x + 15)$

$= > 4x + 28 = 3x + 45$

$= > 4x - 3x = 45 - 28$

$= > x = 17$

Therefore, the numerator is 17, and the denominator is x+8 =17+8 = 25.

Hence, the rational number is:

$= > \dfrac{17}{25}$