NIMCET 2020 — Reasoning PYQ

Step 1: Define the variables

Let the original fraction be $\frac{x}{y}$, where $x$ is the numerator and $y$ is the denominator.

Step 2: Apply the percentage changes

• New Numerator: The numerator is increased by 2026%, which can be written as:

  $$x+25\%\text{ of }x=1.25x=\frac{5}{4}x$$

• New Denominator: The denominator is decreased by 20%, which can be written as:

  $$y-20\%\text{ of }y=0.80y=\frac{4}{5}y$$

Step 3: Set up the equation

According to the problem, the new fraction equals $\frac{5}{4}$:

$$\frac{\frac{5}{4}x}{\frac{4}{5}y}=\frac{5}{4}$$

Step 4: Solve for the original fraction $\frac{x}{y}$

Simplify the left side of the equation by multiplying by the reciprocal:

$$\left(\frac{5}{4}\times \frac{5}{4}\right)\times \frac{x}{y}=\frac{5}{4}$$

$$\frac{25}{16}\times \frac{x}{y}=\frac{5}{4}$$

Now, isolate $\frac{x}{y}$ by multiplying both sides by $\frac{16}{25}$:

$$\frac{x}{y}=\frac{5}{4}\times \frac{16}{25}$$

$$\frac{x}{y}=\frac{4}{5}$$

Therefore, the original value of the fraction is $\frac{4}{5}$.