Correct Answer - Option 4 :
\(\frac{{91}}{{100}}\)
Given:
If the numerator of a fraction is increased by 20% and the denominator is decreased by 30%, the fraction obtained is 39/25
concept used:
Percentage
Calculation:
Let the fraction be x/y
AS per the question,
⇒ \(\frac{{x + \frac{{20x}}{{100}}}}{{y - \frac{{30y}}{{100}}}} = \frac{{39}}{{25}}\)
⇒ \(\frac{{\frac{{6x}}{5}}}{{\frac{{7y}}{{10}}}} = \frac{{39}}{{25}}\)
⇒ \(\frac{{6x}}{{7y}} = \frac{{39}}{{25}} \times \frac{5}{{10}}\)
⇒ \(\frac{x}{y} = \frac{{39}}{{50}} \times \frac{7}{6}\)
⇒ \(\frac{x}{y} = \frac{{273}}{{300}}\)
∴ \(\frac{x}{y} = \frac{{91}}{{100}}\)
∴ The original fraction is 91/100