If the numerator of a fraction is decreased by 10% and the denominator is increased by 15%, the value of the new fraction becomes 2/5 What is the original fraction?

Correct option is B

Given:

The numerator of a fraction is decreased by 10%

The denominator is increased by 15%

The new fraction becomes $$\frac{2}{5}$$​​

We are to find the original fraction

Solution:

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

10% decrease in numerator → 0.9x

15% increase in denominator → 1.15y

Now, 

​$$\frac{0.9x}{1.15y} = \frac{2}{5} \\ \ \\5 \times 0.9x = 2 \times 1.15y \\ \ \\4.5x = 2.3y\\ \ \\45x = 23y\\ \ \\\frac{x}{y} = \frac{23}{45}$$​​

Thus, Original fraction is $$\frac{23}{45}$$​​