Question

the denominator of a rational number is greater than its numerator by 8. if the numeris increased by 17 and the denominator is decreased by 1, the number obtained is 3/2. find the rational number

Answer 1

⇝ Correct Question :-

The denominator of a rational number is greater than its numerator by 8. If the numerator is increased by 17 and the denominator is decreased by 1, the number obtained is 3/2. Find the Rational number

⇝ Given :-

• The denominator of a rational number is greater than its numerator by 8.

• If the numerator is increased by 17 and the denominator is decreased by 1, the number obtained is 3/2.

⇝ To Find :-

• The Rational Number.

⇝ Solution :-

Let Numerator and Denominator of Original Rational Number be :

• Numerator = x

Accordingly :

• Denominator should be = x + 8

So ,

$\text{Original Number = } \frac{\text x}{\text x + 8}$

❒ When Numerator is increased by 17 and the denominator is decreased by 1 :

$\text{Number Becomes : } \frac{\text x + 17}{\text x + 7}$

⏩ According To Question :

$\frac{\text x + 17}{\text x + 7} = \frac{3}{2}$

$:\longmapsto2(\text x + 17) = 3(\text x + 7)$

$:\longmapsto2\text x + 34 = 3\text x + 21$

$:\longmapsto2\text x - 3\text x = 21 - 34$

$:\longmapsto \cancel - \text x = \cancel - 13$

$\purple{ \Large :\longmapsto  \underline {\boxed{{\bf x = 13} }}}$

So,

$\text{Original Number = } \frac{13}{13+ 8}$

Hence,

$\large\underline{\pink{\underline{\frak{\pmb{ Original \: Number = \dfrac{13}{21} }}}}}$

Answer 2

Step-by-step explanation:

Question-

The denominator of a rational number is greater than its numerator by 8. If the numerator is increased by 17 and the denominator is decreased by 1, the number obtained is 3/2. Find the rational number.

Given-

The denominator of a rational number is greater than its numerator by 8. If the numerator is increased by 17 and the denominator is decreased by 1, the number obtained is 3/2.

To find-

The original number.

Solution-

Let,

• Numerator = x
• Denominator = x + 8

$\sf \: Original \: fraction = \frac{x}{x + 8}$

Now,

New Numerator = x + 17

New Denominator = x + 8 - 1 = x + 7

So,

★ According to the question

$\therefore \sf \: \frac{x + 17}{x + 7} = \frac{3}{2} \\ \\ \\☞ \sf \: 3(x + 7) = 2(x + 17) \\ \\ \\ ☞ \sf \: 3x + 21 = 2x + 34 \\ \\ \\ ☞ \sf \: 3x - 2x = 34 - 21 \\ \\ \\ ☞ \sf \: \large \boxed{ \pink{ \bf \: x = 13}}$

So,

• Numerator = x = 13

• Denominator = x + 8 = 13 + 8 = 21

$\large \pink{ \frak{Required \: fraction = \frac{13}{21}} }$

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