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:

Question

Question

This question was previously asked in

SSC Matric Level Previous Paper (Held on: 9 Nov 2020 Shift 1)

Answer 1

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

Alternate Method

If the numerator of a fraction is increased by 20%, It becomes 120% which is given as 39

120% = 39

100% = (39/120) × 100

If the denominator is decreased by 30%, It becomes 70% which is given as 25

70% = 25

100% = (25/70) × 100

Present Fraction = [(39/120) × 100] / [(25/70) × 100] = 91/100