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. plz tell the ans​

Answer 1

⠀⠀⠀⠀⠀⠀⠀${\huge{\underbrace{\rm{Question}}}}$

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. plz tell the ans

⠀⠀⠀⠀⠀⠀⠀⠀${\huge{\underbrace{\rm{Answer}}}}$

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:

Find the rational number

Solution:

Suppose numerator of the rational number is 'P' then denominator is P + 8

Rational number is $\sf{\dfrac{P}{P+8}}$

Numerator is increased by 17 , then it becomes P + 17

Denominator is decreased by 1 , then it becomes P + 8 - 1 = P + 7

Now,

New rational number is

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

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$\sf{:\implies 2P+34=3P+21}$

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$\sf{:\implies 2P-3P=21-34}$

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$\sf{:\implies -P=\:-13}$

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$\boxed{\bf{\pink{:⟹\:P\:=\:13}}}$

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Thus, numerator is 13

Denominator is = P + 8 = 13 + 8 = 21

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Therefore,

$\dashrightarrow\:\:\underline{\boxed{\sf The\:\:\:rational\:\:\:number\:\:\:is\:\:\:\dfrac{13}{21}}}$

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