If A's salary is 25% higher than B's salary, then how much per cent is B's salary lower than that of A's ?

Answer

To solve the problem step by step, we will find out how much percentage B's salary is lower than A's salary, given that A's salary is 25% higher than B's salary.

### Step 1: Define B's Salary
Let B's salary be represented as \( B = 100 \) (this is a convenient choice for calculation).

### Step 2: Calculate A's Salary
Since A's salary is 25% higher than B's salary, we can calculate A's salary as follows:
\[ A = B + 25\% \text{ of } B = 100 + 25\% \text{ of } 100 \]
Calculating 25% of 100:
\[ 25\% \text{ of } 100 = \frac{25}{100} \times 100 = 25 \]
Thus,
\[ A = 100 + 25 = 125 \]

### Step 3: Calculate How Much Lower B's Salary is Compared to A's Salary
Now we need to find out how much lower B's salary is compared to A's salary. We can calculate the difference:
\[ \text{Difference} = A - B = 125 - 100 = 25 \]

### Step 4: Calculate the Percentage Lower
To find out how much percentage B's salary is lower than A's salary, we use the formula:
\[ \text{Percentage lower} = \left( \frac{\text{Difference}}{A} \right) \times 100 \]
Substituting the values we have:
\[ \text{Percentage lower} = \left( \frac{25}{125} \right) \times 100 \]
Calculating this gives:
\[ \text{Percentage lower} = \left( \frac{25}{125} \right) \times 100 = 0.2 \times 100 = 20\% \]

### Final Answer
B's salary is 20% lower than A's salary.

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