If the numerator of a fraction is increased by 80% and the denominator of the fraction is increased by 120%, then the resultant fraction is $$\frac{7}{22}$$​. What is the original fraction?

Correct option is A

Given:

The numerator of a fraction is increased by 80%, and the denominator is increased by 120%. The resultant fraction is $$\dfrac{7}{22}.$$​​

Solution:
Let the original fraction be $$\dfrac{x}{y},$$​ where x is the numerator and y is the denominator.

The numerator is increased by 80%, so the new numerator becomes x + 0.80x = 1.80x.

The denominator is increased by 120%, so the new denominator becomes y + 1.20y = 2.20y.

We are given that the resultant fraction is $$\dfrac{7}{22}$$​, so we can set up the equation:

​$$\frac{1.80x}{2.20y} = \frac{7}{22}$$​

​$$1.80x \times 22 = 7 \times 2.20y$$​

​$$\dfrac{x}{y} =\dfrac{15.4}{39.6} = \dfrac{154}{396} = \dfrac{77}{198} = \dfrac{7}{18}$$​