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 increased by 1 the number obtained 3/2 find the rational number​

Answer 1

Answer:

Appropriate 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 :-

• What is the rational number.

Solution :-

Let,

➲ Numerator = x

➲ Denominator = x + 8

Hence, the required numbers obtained is :

$\implies \sf Original\: Number =\: \dfrac{Numerator}{Denominator}$

$\implies \sf\bold{\pink{Original\: Number =\: \dfrac{x}{x + 8}}}$

According to the question,

$\bigstar$ The numerator is increased by 17 and the denominator is decreased by 1, the number obtained is 3/2.

$\implies \bf \dfrac{Numerator + 17}{Denominator - 1} =\: \dfrac{3}{2}$

$\implies \sf \dfrac{x + 17}{x + 8 - 1} =\: \dfrac{3}{2}$

$\implies \sf \dfrac{x + 17}{x + 7} =\: \dfrac{3}{2}$

By doing cross multiplication we get,

$\implies \sf 3(x + 7) =\: 2(x + 17)$

$\implies \sf 3x + 21 =\: 2x + 34$

$\implies \sf 3x - 2x =\: 34 - 21$

$\implies \sf\bold{\purple{x =\: 13}}$

Hence, the required original fraction is :

$\longrightarrow \sf Original\: Fraction =\: \dfrac{x}{x + 8}$

$\longrightarrow \sf Original\: Fraction =\: \dfrac{13}{13 + 8}$

$\longrightarrow \sf\bold{\red{Original\: Fraction =\: \dfrac{13}{21}}}$

${\small{\bold{\underline{\therefore\: The\: rational\: number\: obtained\: is\: \dfrac{13}{21}\: .}}}}$

Answer 2

Solution:-

• Let the numerator = x

• ∴ Denominator = x + 8

• New numerator = x + 17

• New denominator = (x + 8) – 1 = x + 7

$∴ The \: new \: number = \frac{x + 17}{x + 7}$

According to the condition,we have

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

By cross multiplication,we have

2(x + 17) = 3(x + 7)

2x + 34 = 3x + 21

Transposing 34 to RHS and 3x to LHS, we have

2x – 3x = 21 – 34 => – x = – 13

∴ x = 13 => Numerator = 13

x + 8 = 13 + 8 = 21 => Denominator = 21

$\fbox\pink{∴ The new number = 13/21}$