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 / . Find the rational number​

Answer 1

Answer:

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.
• 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,

$\mapsto \bf Numerator = x$

$\mapsto \bf Denominator =\: x + 8$

Hence, the rational number is :

$\leadsto \sf \dfrac{Numerator}{Denominator}$

$\leadsto \sf\bold{\pink{\dfrac{x}{x + 8}}}$

According to the question,

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

$\implies \sf \dfrac{Numerator + 17}{Denominator - 1} =\: New\: Number$

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

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

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 rational number is :

$\longrightarrow \sf Rational\: Number =\: \dfrac{x}{x + 8}$

$\longrightarrow \sf Rational\: Number =\: \dfrac{13}{13 + 8}$

$\longrightarrow \sf\bold{\red{Rational\: Number =\: \dfrac{13}{21}}}$

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

Answer 2

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.

$\huge{\underline{\mathtt{\red{ƛ}\pink{N}\green{S}\blue{W}\purple{E}\orange{R}}}} \red♡$

Step-by-step explanation:

let numerator be x

The denominator = x+8

=x+17/x+8-1=3/2

=x+17/x+7=3/2

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

=2x+34=3x+21

=34-21=3x-2x

=13=x

=> x/x+8

=13/21

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