Question

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

• A. $\frac{6}{5}$
• B. $\frac{3}{7}$
• C. $\frac{1}{5}$
• D. $\frac{9}{7}$

Answer 1

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

Let the numerator and denominator of a fraction be x and y
We are given that
y -x $=$ 4
y + 1 $=$ 8(x-2)
Then, the equation formed are
y x $=$ 4.......(1)
y + 1 $=$ 8(x 2).......(2)
To solve equation we put y $=$ x+4 in eq(2)
(x+4) +1 $=$ 8x -16
7x $=$ 21
x $=$ 21/7 $=$3
Putting x $=$3 in equation(1) we get
y $=$7
On solving equation (1) and (2) we get
x $=$ 3 and y $=$ 7
Hence, fraction is $\frac{3}{7}$