Question

the denominator of a rational number is greater than its numerator by 7 if numerator is increased by 19 and denominator is decreased by 3 the new number become 4 find the original number
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Answer 1

Answer:-

The Original Rational Number Is $\bf\dfrac{1}{8}$.

Explanation:-

Given:-

• The Denominator of a rational Number is greater than its numerator by 7.

• If the numerator is increased by 19 and denominator is decreased by 4 the result would be equal to 4.

To Find:-

• The original number.

So,

Let the numerator of the rational number be x.

So its denominator will be equal to x + 7.

And The Original Number will be, $\bf\dfrac{x}{x+7}.$

Therefore Acc. To Que.:-

$\tt\mapsto4 = \dfrac{x+ 19}{x + 7 - 3} .$

$\tt\mapsto4 = \dfrac{x + 19}{x + 4}.$

$\tt\mapsto4(x + 4) = x + 19.$

$\tt\mapsto4x + 16 =x + 19.$

$\tt\mapsto4x - x = 19 - 16.$

$\tt\mapsto3x = 3.$

$\tt\mapsto x = \cancel \dfrac{3}{3} .$

$\large \red{\mapsto \boxed{ \blue{ \bf x = 1.}}}$

Therefore The Original Number is,

$\tt= \dfrac{x}{x + 7} .$

$\tt = \dfrac{1}{1 + 7} .$

$\large\red{\boxed{\blue{ \bf = \frac{1}{8}.}}}$

So The Required Rational Number is 1/8.

Answer 2

Given : -

• The denominator of a rational number is greater than its numerator by 7 if numerator is increased by 19 and denominator is decreased by 3 the new number become 4

To find : -

• Original Number

Solution : -

✚ Let the numerator be x then its denominator be (x + 7)

• According to the question

➪ x + 19/x + 7 - 3 = 4

➪ x + 19/x + 4 = 4

➪ 4(x + 4) = x + 19

➪ 4x + 16 = x + 19

➪ 4x - x = 19 - 16

➪ 3x = 3

➪ x = 3/3

➪ x = 1

Hence,

• Numerator = x = 1
• Denominator = (x + 7) = 8
• Required number = numerator/denominator = 1/8