In a fraction, if the numerator is increased by $40 %$ and the denominator is decreased by $20 %$ , then by what percent is the new fraction more or less than the original fraction:

75 %

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60 %

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50 %

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175 %

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Solution

The correct option is D $75 %$ more
Let the fraction be $\frac{x}{y}$
Numerator is increased by 40% and denominator is decreased by 20%.
New numerator $= x + \frac{40 x}{100} = \frac{140 x}{100} = \frac{7 x}{5}$
New Denominator $= y - \frac{20 y}{100} = \frac{4 y}{5}$
New fraction $= \frac{\frac{7 x}{5}}{\frac{4 y}{5}}$
$= \frac{7 x}{4 y}$
Thus, the new fraction is more than the initial fraction by $= \frac{7 x}{4 y} - \frac{x}{y}$
$= \frac{7 x - 4 x}{4 y}$
$= \frac{3 x}{4 y}$
Thus, in percentage = $\frac{3 x}{4 y} \times 100$ %
= $75$ % more than the initial fraction

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In a fraction, if the numerator is increased by 40% and the denominator is decreased by 20%, then by what percent is the new fraction more or less than the original fraction:

In a fraction, if the numerator is increased by $40 %$ and the denominator is decreased by $20 %$ , then by what percent is the new fraction more or less than the original fraction: