Question 57

The numerator of a fraction is decreased by 25% and the denominator is increased by 250%. If the resultant fraction is 6/5 what is the original fraction ?

Solution

Let the original fraction = $$\frac{x}{y}$$

Numerator after 25% decrease = $$x - \frac{25}{100} x = \frac{75x}{100}$$

Denominator after 250% increase = $$y + \frac{250}{100} y = \frac{350y}{100}$$

Acc to ques,

=> $$\frac{\frac{ 75 x }{ 100 }}{\frac{ 350 y }{ 100 }} = \frac{6}{5}$$

=> $$\frac{3x}{14y} = \frac{6}{5}$$

=> $$\frac{x}{y} = \frac{6}{5} \times \frac{14}{3}$$

=> $$\frac{x}{y} = \frac{28}{5}$$

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