Question

please solve my question:

The denominator of a rational number is greater than its numerator by 3. If the number is increased by 16 and the denominator is decreased by 1,then the number obtained is 5/3, find the rational number.​

Answer 1

Answer:

Let the numerator of a rational number be x.

Therefore, denominator = x + 3

according to your question ,

x + 16 / x + 3 -1 = 5/3

or, x + 16 / x + 2 = 5/3

cross multiplication give

5 (x + 2) = 3 (x + 16)

or, 5x + 10 = 3x + 48

or, 5x - 3x = 48 - 10

or, 2x = 38

or, x = 38/2

or, x = 19

Hence, numerator = x = 19

& Denominator = x + 3 = 22

So , rational number = 19/22.

Answer 2

$\bold\blue{Correct \ Question}$

The denominator of a rational number is greater than its numerator by 3. If the numenator is increased by 16 and the denominator is decreased by 1, then the number obtained is 5/3, find the rational number.

$\huge\purple{\underline{\underline{\pink{Ans}\red{wer:-}}}}$

$\sf{Rational \ number \ is \ \frac{19}{22}}$

$\sf\orange{Given:}$

$\sf{\implies{Denominator \ of \ a \ rational \ number}}$

$\sf{is \ greater \ than \ it's \ numerator \ by \ 3.}$

$\sf{\implies{If \ numenator \ is \ increased \ by \ 16 }}$

$\sf{and \ denominator \ is \ decreased \ by \ 1,}$

$\sf{then \ the \ number \ obtained \ is \ \frac{5}{3}}$

$\sf\pink{To \ find:}$

$\sf{Rational \ numbers \ are \ \frac{p}{q} \ form.}$

$\sf{The \ rational \ number.}$

$\sf\green{\underline{\underline{Solution:}}}$

$\sf{Let \ numenator \ be \ x \ and \ denominator}$

$\sf{be \ y.}$

$\sf{According \ to \ first \ condition}$

$\sf{\implies{y-x=3}}$

$\sf{\implies{-x+y=3...(1)}}$

$\sf{According \ to \ second \ condition}$

$\sf{\implies{\frac{x+16}{y-1}=\frac{5}{3}}}$

$\sf{\implies{3(x+16)=5(y-1)}}$

$\sf{\implies{3x+48=5y-5}}$

$\sf{\implies{3x-5y=-53...(2)}}$

$\sf{Multiply \ eq(1) \ by \ 3}$

$\sf{\implies{-3x+3y=9...(3)}}$

$\sf{Add \ equations \ (2) \ and \ (3)}$

$\sf{3x-5y=-53}$

$\sf{+}$

$\sf{-3x+3y=9}$

_______________________

$\sf{\implies{-2y=-44}}$

$\sf{\implies{y=\frac{-44}{-2}}}$

$\sf{\implies{y=22}}$

$\sf{Substitute \ y=22 \ in \ equation (1)}$

$\sf{\implies{-x+22=3}}$

$\sf{\implies{x=22-3}}$

$\sf{\implies{x=19}}$

$\sf{Rational \ number=\frac{x}{y}=\frac{19}{22}}$

$\sf\purple{\tt{\therefore{Rational \ number \ is \ \frac{19}{22}}}}$