Question

he 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 3232. Find the 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 number .

Given :

• 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 numbers.

Solution :

$\longmapsto\tt{Let\:the\:Numerator\:be=x}$

As Given that Denominator is greater than its numerator by 8. So ,

$\longmapsto\tt{Denominator=x+8}$

Now ,

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

$\longmapsto\tt{Numerator=x+17}$

$\longmapsto\tt{Denominator=x+8-1=x+7}$

A.T.Q :

$\longmapsto\tt{\dfrac{x+17}{x+7}=\dfrac{3}{2}}$

$\longmapsto\tt{2(x+17)=3(x+7)}$

$\longmapsto\tt{2x+34=3x+21}$

$\longmapsto\tt{2x-3x=21-34}$

$\longmapsto\tt{{\cancel{-}}1x={\cancel{-}}13}$

$\longmapsto\tt\bf{x=13}$

Value of x is 13..

Therefore :

$\longmapsto\tt\bf{Numerator=13}$

$\longmapsto\tt{Denominator=13+8}$

$\longmapsto\tt\bf{21}$

So , The Fraction is 13/21...

Answer 2

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 number

Given:-

• 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 Numbers... That is given in the question.

Solution :-

• Let the number be = x

• Given that the denominator greater than number 8

• Which means that x + 8

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

$\sf{ \bold{ \underline{numerator = x + 17 }{} }{} }{} \\ \bold{ \sf {denominator = x + 8 - 1 = x + 7}{} }{} \\ \sf{ \sf{ \frac{x + 17 }{x + 7} = }{ \frac{3}{2} } }{} \\ \\ \sf{2(x + 17) = 3(x + 7)}{} \\ \sf{2x + 34 = 3x + 21}{} \\ \\ \sf{2x - 3x = 21 - 34}{} \\ \\ - x = - 13 \\ \sf{x = 13}{}$

• Numerator = 13
• From the question denominator is greater than 8

• So, denominator = 13+8 = 21

• $\sf{ \frac{13}{21} }{ \: is \: the \: fraction}$

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