Question

The denominator of a fraction is greater than the numerator by 3.if 7 is added to the numerator,the fraction increases by unity.find the fraction.

Answer 1

Let the numerator of fraction = x
denominator = x+3
fraction is $\frac{x}{x+3}$

if 7 is added to the numerator,the fraction increases by unity. Thus

$\frac{x+7}{x+3}= \frac{x}{x+3}+1\\ \\ \Rightarrow \frac{x+7}{x+3}= \frac{x+x+3}{x+3}\\ \\ \Rightarrow \frac{x+7}{x+3}= \frac{2x+3}{x+3}\\ \\ \Rightarrow x+7=2x+3\\ \\ \Rightarrow x-2x=3-7\\ \\ \Rightarrow -x=-4\\ \\ \Rightarrow x=4$

Fraction is $\frac{x}{x+3}= \frac{4}{4+3}=\boxed{ \frac{4}{7} }$

Answer 2

i think 4/7 is the answer...The numerator is x so denominator is x+3
So after adding 7 it will be
x+7/x+3=x/x+3+1
x+7/x+3=x+x+3/x+3
x+7/x+3=2x+3/x+3
Since denominators are same. The numerators can be easily compared...
x+7=2x+3
x-2x=3-7
x=4

So Numerator is 4 and denominator is 7