Question

# The numerator of a fraction is $$4$$ less than the denominator. If $$1$$ is added to both its numerator and denominator, it becomes $$\cfrac{1}{2}$$. Find the fraction.

Solution

## Let the fraction be $$\dfrac{a}{b}$$Numerator= denominator-$$4$$$$a=b-4 \Rightarrow b-a=4$$If $$1$$ added to both numerator and denomator then fraction $$=\dfrac{1}{2}$$$$\dfrac{a+1}{b+1}=\dfrac{1}{2}$$$$2a+2=b+1$$$$2a-b=-1$$$$(2a-b)+(b-a)=4-1$$$$a=3 , b=7$$ Fraction$$= \dfrac{3}{7}$$Mathematics

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