Question

After an increment of 7 in both the numerator and denominator, a fraction changes to 3/4. find the original fraction.

Answer 1

Answer:

The original fraction is $\frac{2}{5}$.

Step-by-step explanation:

Let the original fraction be $\frac{x}{y}$.

It is given that after an increment of 7 in both the numerator and denominator, a fraction changes to $\frac{3}{4}$.

$\frac{x+7}{y+7}=\frac{3}{4}$

$4(x+7)=3(y+7)$

$4x+28=3y+21$

$4x+7=3y$

There are many possible fractions that can satisfy the above equation. Find the minimum value of x for which the the value of y is an integer.

Put x=1

$4(1)+7=3y$

$y=\frac{11}{3}$

Which is not an integer.

Put x=2

$4(2)+7=3y$

$y=5$

Therefore the original fraction is $\frac{2}{5}$.

Answer 2

Step-by-step explanation:

Let the numerator be N and the denominator be

D, so that fraction is N/D.

After an increase of 7 in both numerator as well as the denominator, the fraction changes to 3/4

(N+7)/(D+7) =3/4

3D-4N=7

Two variables and one equation.

Hence more than one solution possible.

Possible solutions (N,D) are:

(2,5) (5,9), (8,13), (11,17), (14,21), (17,25), (20,29), (23, 33) so on

In general,

(2+3a, 5+4a) for a= 1, 2, 3

Here are some results upto a = 25