Question

the denominator of a rational number is greater than its numerator by 4 . If numerator is increased by 11 and the denominator is decreased by 1 , the new number becomes 7/3 . Find the original number . ​

Answer 1

Answer:

According to 1st statement

x/x+4

According to 2nd statement

x+11/(x+4)-1=7/3

x+11/x+3=7/3

3x+33=7x+21

7x-3x=33-21

4x=12

x=3

Original Number=3/3+4

Using 1st statement

=3/7

Answer 2

Given:

• The denominator of a rational number is greater than it's numerator by 4. If the numerator is increased by 11 and the Denominator is decreased by 1, the new number becomes ⁷⁄₃.

To find:

•  The Original number

Solution:⠀⠀

Let's say, that the numerator of the fraction be x. Then, denominator of the fraction be (x + 4) respectively.

⠀

$\begin{gathered}\sf \orange\bigstar \: {According \;to\;the\; Question\; :}\end{gathered}$

If the numerator is increased by 11 and the Denominator is decreased by 1, the new number becomes ⁷⁄₃.

⠀⠀

$\begin{gathered} : \implies\sf\Bigg\{\dfrac{x + 11}{x + 4 - 1}\Bigg\} = \Bigg\{\dfrac{7}{3}\Bigg\}\\\\ : \implies\sf\Bigg\{\dfrac{x + 11}{x + 3}\Bigg\} = \Bigg\{\dfrac{7}{3}\Bigg\}\\\\ : \implies\sf 3\Big\{x + 11\Big\}=7\Big\{x + 3\Big\}\\\\ : \implies\sf 3x + 33 = 7x + 21 \\\\ : \implies\sf 3x - 7x = 21 - 33\\\\ : \implies\sf -4x = -12\\\\:\implies \sf x = \cancel\dfrac{-12}{-4}\\\\ : \implies\underline{\boxed{{\frak{x = 3}}}}\; \pink\bigstar\end{gathered}$

Therefore,

• Numerator of the fraction, x = 3
• Denominator of the fraction, (x + 4) = (3 + 4) = 7 

$\boxed{\sf{Hence,\: the \;original\; number\; is\;\bf{\dfrac{3}{7}}}}.$

Thank you!

@itzshivani