Question

a. The denominator of a fraction is greater than its numerator by 9. If 7 is subtracted
from both, its numerator and denominator, the fraction becomes 2. Find the
original fraction
3 [3m]​

Answer 1

$\huge\bf\underline\mathfrak{Corrected \: Question :}$

The denominator of a fraction is greater than it's numerator by 9. If 7 is subtracted from both it's numberator and denominator, the new fraction becomes 2/3. Find the original fraction.

$\huge\bf\underline\mathfrak{Answer :}$

• $\text {The required fraction is 25/34 ✓}$.

$\huge\bf\underline\mathfrak{Concept :}$

• Solving simple equations with opening brackets and with the help of cross-multiplication method.

$\huge\bf\underline\mathfrak{Step \: by \: step \: explanation :}$

$\huge\bf\underline\mathfrak{Given :}$

• $\text {Denominator is greater than the numerator by 9.}$
• The fraction becomes 2/3 if 7 is subtracted from the both numerator and denominator.

$\huge\bf\underline\mathfrak{To \: find :}$

• $\text {Original fraction.}$

$\huge\bf\underline\mathfrak{Solution :}$

$\underline\text {From the given conditions :-}$

$\text {Let the original fraction be in the form of p/q.}$

$\text {Let numerator be p.}$

$\implies\text {Denominator of the fraction = p+9.}$

• Since, it is said that denominator is greater than numerator by 9, we have taken denominator as p+9.

$\bf\underline {Now, \: according \: to \: question :-}$

$\underline\text {It is given that :-}$

• When 7 is subtracted from both numerator and denominator, then the fraction becomes 2/3.

$\implies\bf\ \frac{( \: p - 7 \: )}{( \: p \: + \: 9 \: ) - 7} = \frac{2}{3}$

• Opening brackets.

$\implies\bf\ \frac{p - 7}{p + 9 - 7} = \frac{2}{3}$

$\implies\bf\ \frac{p - 7}{p + 2} = \frac{2}{3}$

• On cross-multiplying.

$\implies\bf\ 3(p - 7) = 2(p + 2)$

$\implies\bf\ 3p - 21 = 2p + 4$

• Moving all the variable in the left hand side and all the variables on the right hand side.

$\implies\bf\ 3p - 2p = 4 + 21$

$\implies\bf\boxed {p = 25}$

$\underline\text { Putting the value of p in the fraction :-}$

$\bf\text {Numerator = p = 25, and}$

$\bf\text {Denominator = p+9 = 25+9 = 34}$

$\underline\mathfrak {∴ \: Required \: Fraction = 25/34}$