Question

the denominator of a rational number is greater than its numerator by 5 if the numerator is increased by 8 and denominator is decreased by 1 the new number becomes 5/3 find the original number​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

The Original Rational Number is $\dfrac{2}{7}$

Step-by-step explanation:

Given :

Denominator is = greater than its numerator by 5

Numerator when increased by 8 and denominator when decreased by 1, new fraction = $\dfrac{5}{3}$

To find :

The Original Rational Number

Solution :

$\textbf{\small{\underline{Let the - }}}$

• Numerator be x
• Denominator be (x + 5)

$\textbf{\small{\underline{According to the Question - }}}$

Numerator when increased by 8 and denominator when decreased by 1, new fraction = $\dfrac{5}{3}$

★ $\boxed{\bf{\frac{x + 8}{(x + 5) - 1} = \frac{5}{3}}}$

$\sf{\implies} \:\frac{x + 8}{(x + 5) - 1} = \frac{5}{3} \\ \sf{\implies} \: \frac{x + 8}{x + 4} = \frac{5}{3} \\ \sf{\implies} \:3(x + 8) = 5(x + 4) \\ \sf{\implies} \:3x + 24 = 5x + 20 \\ \sf{\implies} \:5x - 3x = 24 - 20 \\ \sf{\implies} \:2x = 4 \\ \sf{\implies} \:x = \frac{4}{2} \\ \sf{\implies} \:x = 2$

$\rule{300}{1.5}$

★ Value of (x + 5)

$\sf{\implies} \:2 + 5 \\ \sf{\implies} \:7$

• Numerator = 2
• Denominator = 7

Original Rational Number = $\boxed{\boxed{\sf{\frac{2}{7}}}}$

$\therefore$ The Original Rational Number is $\dfrac{2}{7}$