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The salary of Krish is [tex]$25\%$[/tex] more than the salary of Bipul. By what percentage is the salary of Bipul less than the salary of Krish?

A. [tex]$3.25\%$[/tex]
B. [tex]$16 \frac{2}{3}\%$[/tex]
C. [tex]$22 \frac{1}{2}\%$[/tex]
D. [tex]$20\%$[/tex]


Sagot :

Let's break down the problem step by step to determine the percentage by which Bipul's salary is less than Krish's salary.

1. Understanding the relationship between their salaries:
- Let's denote Krish's salary by [tex]\( K \)[/tex] and Bipul's salary by [tex]\( B \)[/tex].
- According to the problem, Krish's salary is 25% more than Bipul's salary.
- Mathematically, this means: [tex]\( K = B + 0.25B \)[/tex].
- Simplifying this, we get: [tex]\( K = 1.25B \)[/tex].

2. Finding the difference between the salaries:
- The difference in their salaries is given by [tex]\( K - B \)[/tex].
- Substituting [tex]\( K = 1.25B \)[/tex], we get: [tex]\( K - B = 1.25B - B \)[/tex].
- Simplifying this, we obtain: [tex]\( K - B = 0.25B \)[/tex].

3. Calculating the percentage by which Bipul's salary is less than Krish's salary:
- Now, we need to express this difference in terms of a percentage of Krish's salary [tex]\( K \)[/tex].
- The percentage difference is calculated as:
[tex]\[ \text{Percentage difference} = \left( \frac{\text{Difference in salary}}{\text{Krish's salary}} \right) \times 100 \][/tex]
- Substituting the known values, we get:
[tex]\[ \text{Percentage difference} = \left( \frac{0.25B}{1.25B} \right) \times 100 \][/tex]
- Simplifying the fraction inside the parentheses:
[tex]\[ \text{Percentage difference} = \left( \frac{0.25}{1.25} \right) \times 100 \][/tex]
- Further simplifying [tex]\( \frac{0.25}{1.25} \)[/tex], we get:
[tex]\[ \frac{0.25}{1.25} = 0.2 \][/tex]
- Therefore, the percentage difference is:
[tex]\[ 0.2 \times 100 = 20\% \][/tex]

Thus, Bipul's salary is 20% less than Krish's salary. The correct answer is:

d. [tex]\( 20\% \)[/tex]
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