Question

the denominator of a rational number number is gratter than its numerator by 6 if the numerator is increased by 5 and denominator is decreased by 3 the number obtained is 5/4 find the rational no
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Answer 1

Question:

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

Answer:

Given:

• Denominator is greater than numerator by 6
• Numerator increased 5 and denominator decreased 3, obtained number is 5/4

To Find:

• Rational number?

Solution:

[Case 1]:

Let suppose that numerator of rational number is x

$\therefore$ Denominator = (x + 6)

Formed number is: $\small\bf\dfrac{x}{(x+6)}$

[Case 2]:

Adding 5 and subtracting 3 from numerator and denominator respectively ••••(as given in question)

$\small\bf\dfrac{x}{(x+6)}$

$\implies\small\bf\dfrac{x+5}{x+6-3}~=~\dfrac{5}{4}$

$\implies\small\bf\dfrac{x+5}{x+3}~=~\dfrac{5}{4}$

On cross multiplication:

$\implies\small{\bf{4(x+5)~=~5(x+3)}}$

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

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

$\implies$ -x = -5

$\implies$ x = 5

So, numerator is 5

$\therefore$ denominator = 5+6 = 11

Formed rational number :

$\small\bf\dfrac{5}{11}$