Question

Q9) A fraction becomes 1/3 when 1 is subtracted from the numerator and it
becomes 14 when 8 is added to its denominator. Find the fraction.​

Answer 1

Let the numerator = x

And the denominator = y

So, the fraction

$= \frac{x}{y}$

According to the question,

Condition I:

$\frac{x - 1}{y} = \frac{1}{3}$

$= > 3(x - 1) = y$

$= > 3x - y = y$

$= > 3x - y - 3 = 0..(i)$

Condition II:

$\frac{x}{y + 8} = \frac{1}{4}$

$= > 4x = y + 8$

$= > 4x - y = 8$

$= > 4x - y - 8 = 0..(ii)$

By cross - multiplication method, we have

$= > \frac{x}{8 - 3} = \frac{y}{ - 12 + 24} = \frac{1}{ - 3 + 4}$

$= > \frac{x}{5} = \frac{y}{12} = \frac{1}{1}$

I II III

On taking I and III ratio, we get

$\frac{x}{5} = \frac{1}{1}$

$= > x = 5$

On taking II and III ratio, we get

$= > \frac{y}{12} = \frac{1}{1}$

$= > y = 12$

So, the numerator is 5 and the denominator is 12

Hence, the fraction is

$\frac{5}{12}$