Question

The denominator of a rational number is greater than its numerator by 6.If

the numerator is increased by 5 and the denominator by 3,then number

obtained is 5/4.Find the rational number.

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Answer 1

Answer:

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Answer 2

Answer :

• 5 / 11

Given :

• The denominator of a rational number is greater than its numerator by 6.If   the numerator is increased by 5 and the denominator is decreased by 3,then number  obtained is 5/4.

To Find :

• Rational number

Solution :

Let the numerator be " x "

Denominator be " y "

A/c , " The denominator of a rational number is greater than its numerator by 6 "

⇒ y = x + 6

⇒ y - x = 6

⇒ 4y - 4x = 24 ... (1) [ Multiply with 4 on both sides ]

A/c , " The numerator is increased by 5 and the denominator by 3,then number  obtained is 5/4 "

$\implies \bf \dfrac{x+5}{y-3}=\dfrac{5}{4}\\\\\implies \bf 4x+20=5y-15\\\\\implies \bf 5y-4x=35...(2)$

Now solve (1) - (2) , we get ,

⇒ ( 4y - 4x ) - ( 5y - 4x ) = 24 - 35

⇒ - y = - 11

⇒ y = 11

sub. y value in (2) , we get ,

⇒ 4 x = 5 ( 11 ) - 35

⇒ 4 x = 20

⇒ x = 5

So , the rational number is x/y = 5/11