Question

The denominator of a rational number is greater than its numerator by 7.If the numerator is increased by 13 and denominator is decreased by 2 ,the number obtained is 4/3.Find the rational number. ​

Answer 1

Answer :

• Rational number is 19/26

Given that :

• The denominator of a rational number is greater than its numerator by 7
• If the numerator is increased by 13 and denominator is decreased by 2 , the number obtained is 4/3

To find :

• Rational number

Solution :

• Let the numerator of rational number be x

The denominator of a rational number is greater than its numerator by 7 so,

• Let the denominator be x + 7

Then rational number becomes = x / x + 7

According to question

Given that, If the numerator is increased by 13 and denominator is decreased by 2 ,the number obtained is 4/3 so,

➠ x + 13 / x + 7 - 2 = 4/3

➠ x + 13 / x + 5 = 4/3

➠ 3(x + 13) = 4(x + 5)

➠ 3x + 39 = 4x + 20

➠ 3x - 4x = 20 - 39

➠ - x = - 19

➠ x = 19

Finding the rational number :

➠ x / x + 7

➠ 19 / 19 + 7

➠ 19/26

Hence ,Rational number is 19/26

Answer 2

ɢɪᴠᴇɴ :

• The denominator of rational number is greater than its numerator by 7

• If the numerator is increased by 13 and denominator is decreased by 2 , The number obtained is 4 / 3

Tᴏ ғɪɴᴅ :

• Find the rational number.

$\: \: \: \: \: \: \: \: ▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁$

$\sf{ \: \: \: \: \: \: \: \: \: Let \: the \: numerator \: be " x "}$

$\sf{ \: \: \: \: \: \therefore \: Denominator \: will \: be " x + 7"}$

$\begin{gathered} \: \: \: \: \: \: \: \: \: \: \: \: \: \dag \: \: \: \: { \underline{ \frak{According \: to \: question}}} \end{gathered}$

$\: \: \: \: \: \: \underline{ \boxed{ \sf{ \pmb{Equation = \frac{x + 13}{x + 7 - 2} = \frac{4}{3} }}}}$

$\begin{gathered} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \implies \sf{3 \times (x + 13) = 4\:( x + 7 -2)} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf : \implies \: 3x + 39 = 4x + 20 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf : \implies \: 39 - 20 = 4x - 3x \\ \\ \underline{ \boxed {\pink{ \sf : \implies \: x = 19}}}\end{gathered}$

$\: \: \: \: \: \: \: \: ▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁$

$\sf{Numerator = x = 19}$

$\sf{Denominator = x + 7 = 28 }$

$\sf{Fraction = \frac{19}{28} }$