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If the numerator of a fraction is increased by 20% and the denominator is decreased by 30%, the fraction obtained is \(\frac{{39}}{{25}}\). The original fraction is:
1. \(\frac{{67}}{{75}}\)
2. \(\frac{{100}}{{91}}\)
3. \(\frac{{75}}{{68}}\)
4. \(\frac{{91}}{{100}}\)

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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

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