Question

the denominator of a rational number is greater than its numerator by 3 . If 3 is subtracted from the numerator and 2 is added to the denominator , the new number is 1/5 . find the original number

Answer 1

Answer:

Answer. It is given that if 3 is subtracted from the numerator and 2 is added to its denominator, then new number becomes 1/5.

Answer 2

$\large{\textbf{\textsf{\underline{\red{Given}}{\red{:}}}}}$

• The denominator of a rational number is greater than its numerator by 3
• If 3 is subtracted from the numerator and 2 is added to the denominator, the new number is $\sf~{\dfrac{1}{5}}$

$\large{\textbf{\textsf{\underline{\red{To~find}}{\red{:}}}}}$

• The original number

$\large{\textbf{\textsf{\underline{\red{Solution}}{\red{:}}}}}$

• Let the numerator of the rational number be x

$\implies$ Denominator = x + 3

$\therefore{{\sf{\pmb{Rational~number}}} = {\sf{\pmb{{\dfrac{x}{x+3}}}}}}$

Also Given :

• If 3 is subtracted from the numerator and 2 is added to the denominator, the new number is $\sf~{\dfrac{1}{5}}$

$\sf\implies{{\dfrac{x-3}{(x+3)+2}}={\dfrac{1}{5}}}$

$\sf\implies{5(x-3)=(x+3)+2~~~~~~~~~~(Cross~multiplying)}$

$\sf\implies{5x-15=x+5}$

$\sf\implies{5x-x=5+15}$

$\sf\implies{4x=20}$

$\sf\implies{x={\dfrac{20}{4}}}$

$\sf\implies{x={\red{\underline{\boxed{\sf{\pmb{~5~}}}}}}}$

$\large \therefore \: {\textbf{\textsf{\underline{\red{Required~answer}}{\red{:}}}}}$

• x = 5

$\therefore{{\sf{\pmb{Rational~number}}} = {\sf{{\dfrac{x}{x+3}}}}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf \implies \frac{5}{5 + 3} \\ \\ \sf \implies { \red{ \underline{ \boxed{ \pmb{ \: \frac{5}{8} \: }}}}} \: \: \:$