Question

the denominator of a rational number is greater than ots numerator by 10 if numerator is increased by 19 and the denominator is decreased by 1, then the nu5 obtained is 3/2 find the original number

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Answer 1

Answer:

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Step-by-step explanation:

Let the numerator be x.

⇒  Then, denominator will be =x+10

According to the question,

⇒   x+19  / x+10−1  = 3/2

⇒    x+19  / x+9  = 3/2

⇒  2(x+19)=3(x+9)

⇒  2x+38=3x+27

⇒  x=38−27

⇒  x=11

⇒  The required rational number =  x/x+10  = 11/11+10 =  11/21

Answer 2

Step-by-step explanation:

Given:-

• The denominator of a fraction is 10 more than the numerator.

• If the numerator is increased by 19 and denominator is decreased by 1 the fraction becomes 3/2.

To Find:-

• The original fraction.

Solution:-

Let the numerator be x

The denominator = x + 10

The original fraction = $\rm \dfrac{x}{x+10}$

If the numeratorator is increased by 19

The numerator becomes x + 19

If the denominator is decreased by 1

The denominator becomes x + 10 - 1 = x + 9

The fraction becomes 3/2

So:-

$\rm \dashrightarrow \dfrac{x+19}{x+9} = \dfrac{3}{2}$

By cross multiplication:-

$\rm \dashrightarrow 2(x+19) = 3(x+9)$

$\rm \dashrightarrow 2x + 38 = 3x + 27$

$\rm \dashrightarrow 3x - 2x = 38 - 27$

$\rm \dashrightarrow x = 11$

The numerator = x = 11

The denominator = x + 10 = 11 + 10 = 21

The fraction = $\rm \dfrac{x}{x+10}$

$\underline{\boxed{\purple{\rm \therefore The \: original \: fraction = \dfrac{11}{21}}}}$