P’s salary is 20% lower than Q’s salary which is 20% lower than R’s salary. By how much percent is R’s salary more than P’s salary?

The correct option is 56.25%.

Let us break down the problem step-by-step to understand how to arrive at this answer.

Step 1: Define a starting value for R's salary.
To make calculations straightforward, let us assume R's salary is 100 units.
Let R's salary = $R=100$.

Step 2: Calculate Q's salary.
The problem states that Q's salary is 20% lower than R's salary.
Therefore, we calculate Q's salary as:
$Q=R-(20\%\text{ of }R)$
$Q=100-(0.20\times 100)$
$Q=100-20=80$.

Step 3: Calculate P's salary.
We are told that P's salary is 20% lower than Q's salary.
Using Q's salary (80), we calculate P's salary as:
$P=Q-(20\%\text{ of }Q)$
$P=80-(0.20\times 80)$
$P=80-16=64$.

Step 4: Find by how much percent R's salary is more than P's salary.
We need to compare R's salary (100) with P's salary (64).
The absolute difference between R's salary and P's salary is:
$\text{Difference}=R-P=100-64=36$.
To find the percentage by which R is more than P, we divide this difference by P's salary and multiply by 100:
$\text{Percentage Increase}=\left(\frac{R-P}{P}\right)\times 100$
$\text{Percentage Increase}=\left(\frac{36}{64}\right)\times 100$
Simplifying the fraction:
$\frac{36}{64}=\frac{9}{16}$
Calculating the percentage:
$\frac{9}{16}\times 100=0.5625\times 100=56.25\%$.

Thus, R's salary is 56.25% more than P's salary.