Question

The denominator of a rational number is greater than its numerat or by 6 . If the numerator is increased by 9 and denominator is decreased by 3,then new rational number obtain is 5/2. Find the rational number

Answer 1

To find :

• we need to find the rational number.

Given :

• Denominator of rational number is greater than it's numerator by 6.

• If the numerator is increased by 9 and denominator is decreased by 3,then new rational number obtain is 5/2.

Let the numerator be x and denominator be y

• Rational number = x/y

$\underline{ \large{ \mathscr{\dag\:A \bf{ccourding} \: to \: \mathscr {Q} \bf{uestion} ....}}}$

Denominator of rational number is greater than it's numerator by 6.

So,

• Denominator = x + 6

The numerator is increased by 9 and denominator is decreased by 3, then new rational number obtain is 5/2.

⟶ (x + 9)/x + 6 - 3 = 5/2

⟶ (x + 9)/x + 3 = 5/2

⟶ 2(x + 9) = 5(x + 3)

⟶ 2x + 18 = 5x + 15

⟶ 18 - 15 = 5x - 2x

⟶ 3 = 3x

⟶ x = 1

So,

⚘ Numerator of rational number x = 1

⚘ Denominator of rational number = y

= x + 6

= 1 + 6

= 7

• Rational number = 1/7

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