Question

The numerator of a fraction is 4 less than the denominator. If the numerator is decreased by 2 and denominator is increased by 1, then the denominator is eight times the numerator. Find the fraction. ​

• A. $\frac{5}{9}$
• B. $\frac{9}{5}$
• C. $\frac{3}{7}$
• D. $\frac{7}{3}$

Answer 1

The correct option is C $\frac{3}{7}$

Let’s assume the numerator of the fraction to be x and the denominator of the fraction to be y.​
So, the required fraction is x/y.​
From the question it’s given as,​
The numerator of the fraction is 4 less the denominator.​
Thus, the equation so formed is,​
$x=y–4$
$\Rightarrow x–y=-4$ …… (i)​
And also it’s given in the question as,​
If the numerator is decreased by 2 and denominator is increased by 1, then the denominator is 8 times the numerator.​
Putting the above condition in an equation, we get​
$y+1=8(x-2)$
$\Rightarrow y+1=8x–16$
$\Rightarrow 8x–y=1+16$​
$\Rightarrow 8x–y=17$…… (ii)​
Subtracting the equation (ii) from (i), we get​
$(x–y)–(8x–y)=–4–17$
$\Rightarrow x–y-8x+y=-21$
$\Rightarrow -7x=-21$
$\Rightarrow x=\frac{21}{7}$
$\Rightarrow x=3$​
Substituting the value of x in the equation (i), we get,​
$3–y=–4$
$\Rightarrow y=3+4$
$\Rightarrow y=7$
Therefore, the fraction is $\frac{3}{7}$.​