Question

The denominator of a rational number is 4 more than its numerator. If 11 is added to the numerator and 1 is subtracted from the denominator, the new number is 7/3. Find the original number.​

Answer 1

Answer:

Let the numerator be x

Denominator be x+4

$Orignal \: \: fraction= \frac{x}{x + 4}$

According to question

$= \frac{x + 11}{x + 4 - 1} = \frac{7}{3}$

$= \frac{x + 11}{x + 3} = \frac{7}{3}$

$= 3(x + 11) = 7(x + 3)$

$= 3x + 33 = 7x + 21$

$7x - 3x = 33 - 21$

$4x = 12$

$x = \frac{12}{4}$

$x = 3$

Numerator=3

Denominator=x+4

=3+4

=7

Orignal fraction=3/7

Let's verify

$\frac{3 + 11}{7 - 1} = \frac{7}{3}$

$\frac{14}{6} = \frac{7}{3}$

$\frac{7}{3} = \frac{7}{3}$

Since LHS=RHS

Hence the given solution,

$Orignal \: \: Fraction = \frac{3}{7}$