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The difference between the numerator and the denominator of a fraction is 5. If 5 is added to its denominator, the fraction is decreased by $$1\frac{1}{4}$$. Find the value of the fraction.

The difference between the numerator and the denominator of a fraction is 5. If 5 is added to its denominator, the fraction is decreased by $$1\frac{1}{4}$$. Find the value of the fraction. Correct Answer $$2\frac{1}{4}$$

Let the denominator be x
Then, numerator = x + 5
Now,
$$\eqalign{ & \Leftrightarrow \frac{{x + 5}}{x} - \frac{{x + 5}}{{x + 5}} = \frac{5}{4} \cr & \Leftrightarrow \frac{{x + 5}}{x} = \frac{5}{4} + 1 \cr & \Leftrightarrow \frac{{x + 5}}{x} = \frac{9}{4} \cr & \Leftrightarrow \frac{{x + 5}}{x} = 2\frac{1}{4} \cr} $$
So, the fraction is $$2\frac{1}{4}$$

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