Question

The denominator of a fraction is greater than its numerator by $7$. If $4$ is added to both its numerator and denominator, then it becomes $\frac{1}{2}$. Find the fraction.

• A. $\frac{1}{6}$
• B. $\frac{7}{3}$
• C. $\frac{3}{10}$
• D. $\frac{6}{7}$

Answer 1

The correct option is C $\frac{3}{10}$

Let the numerator of a fraction be x and denominator be y
Hence the fraction $=\frac{x}{y}$
According to the problem
Case 1
y$=$x+7
xy$=$7.......(1)
Case2
$\frac{x+4}{y+4}=\frac{1}{2}$
2x+8$=$y+4
2xy$=$4....(2)
Subtracting equation(2) from equation(1)
xy$=$7
2xy$=$4
-----------------
x$=$3
x$=$3
Substitute x$=$3 in equation (i)
3y$=$7
y$=$10
Hence the fraction is$\frac{Numerator}{Denominator}\frac{x}{y}=\frac{3}{10}$