Question

The denominator of a rational number is greater than its numerator by 7. if 3 is subtracted from the numerator and 2 is added to its denominator,the new number becomes 1/5.Find the

rational number

Answer 1

here is the answer of your question

Answer 2

$\sf\small\underline\purple{Let:-}$

$\sf{\implies Numerator\:_{(fraction)}=N}$

$\sf{\implies Denominator\:_{(fraction)}=D}$

$\sf{\implies Rational\: number=\dfrac{N}{D}}$

$\sf\small\underline\purple{Given:-}$

$\sf{\implies Denominator=Numerator+7}$

$\sf\small\underline\purple{To\: Find:-}$

$\sf{\implies The\:ratio\: number=?}$

$\sf\small\underline\purple{Solution:-}$

$\bf\small\underline{Calculation\:for\:1st\: equation:-}$

$\sf{\implies Rational\: number\:_{(denominator)}=Rational\: number\:_{(numerator)}+7}$

$\tt{\implies D=N+7----(i)}$

$\bf\small\underline{Calculation\:for\:2nd\: equation:-}$

$\sf{\implies \dfrac{Numerator-3}{Denominator+2}=Rational\: number\:_{(become\:1/5)}}$

$\tt{\implies \dfrac{N-3}{D+2}=\dfrac{1}{5}}$

$\tt{\implies 5N-15=D+2}$

$\tt{\implies 5N-D=2+15}$

$\tt{\implies 5N-D=17-----(ii)}$

In eq (ii) putting the value of D=N+7:-]

$\tt{\implies 5N-(N+7)=17}$

$\tt{\implies 5N-N-7=17}$

$\tt{\implies 5N-N=17+7}$

$\tt{\implies 4N=17+7}$

$\tt{\implies 4N=24}$

$\tt{\implies N=\frac{24}{4}=6}$

Putting the value of N=6 in eq (i):-]

$\tt{\implies D=N+7}$

$\tt{\implies D=6+7}$

$\tt{\implies D=13}$

$\sf\large{Hence,}$

$\sf{\implies Rational\: number=\frac{N}{D}}$

$\bf{\implies Rational\: number=\frac{6}{13}}$