Two numbers are `10%` and `25%` leaser than a third number. By how much percent is the second number to be enhanced to make it equal to the first number?

Options

A. 16.67 percent.
B. 20 percent.
C. 15 percent.
D. 60 percent.

Answer

To solve the problem step by step, we can follow these steps:

### Step 1: Define the Third Number
Let’s assume the third number is \( C = 100 \).

### Step 2: Calculate the First Number
The first number \( A \) is 10% less than the third number \( C \).
\[ A = C - 10\% \text{ of } C = 100 - 10\% \text{ of } 100 = 100 - 10 = 90 \]

### Step 3: Calculate the Second Number
The second number \( B \) is 25% less than the third number \( C \).
\[ B = C - 25\% \text{ of } C = 100 - 25\% \text{ of } 100 = 100 - 25 = 75 \]

### Step 4: Find the Difference Between the Two Numbers
Now, we need to find the difference between the first number \( A \) and the second number \( B \).
\[ \text{Difference} = A - B = 90 - 75 = 15 \]

### Step 5: Calculate the Percentage Increase Required
To find out by how much percent the second number \( B \) needs to be enhanced to make it equal to the first number \( A \), we use the formula for percentage increase:
\[ \text{Percentage Increase} = \left( \frac{\text{Difference}}{B} \right) \times 100 \]
Substituting the values we have:
\[ \text{Percentage Increase} = \left( \frac{15}{75} \right) \times 100 = 20\% \]

### Conclusion
The second number needs to be enhanced by **20%** to make it equal to the first number.

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