The denominator of a fraction is 3 more than the numerator. If the numerator as well as the denominator are increased by 4, the fraction becomes $$\frac{4}{5}$$​ then what was the original fraction?

Correct option is D

Given:
Let the numerator of the original fraction be  x .
The denominator is 3 more than the numerator, so the denominator is  x + 3 .
When both the numerator and denominator are increased by 4, the new fraction becomes $$\frac{4}{5}$$.​

Solution:
Let the original fraction be $$\frac{x}{x + 3}$$​​
After increasing the numerator and denominator by 4, the new fraction is:
$$\frac{x + 4}{x + 3 + 4} = \frac{x + 4}{x + 7}$$

Now,

$$\frac{x + 4}{x + 7} = \frac{4}{5}$$​​

5x + 20 = 4x + 28
5x - 4x + 20 = 28
x + 20 = 28
x = 28 - 20
x = 8

Now,

$$\frac{x}{x + 3} = \frac{8}{8 + 3} = \frac{8}{11}$$​​