Two numbers are respectively 25% and 20% less than a third number. What per cent is the first number of the second ?

Options

A. 0.05
B. 0.75
C. 0.8
D. 0.9375

Answer

To solve the problem step by step, we will first define the numbers based on the information given and then calculate the required percentage.

### Step 1: Define the Third Number
Let the third number be \( x \).

### Step 2: Calculate the First Number
The first number is 25% less than the third number. Therefore, we can calculate the first number as follows:
\[ \text{First Number} = x - 0.25x = 0.75x \]

### Step 3: Calculate the Second Number
The second number is 20% less than the third number. Therefore, we can calculate the second number as follows:
\[ \text{Second Number} = x - 0.20x = 0.80x \]

### Step 4: Find What Percent the First Number is of the Second Number
We need to find out what percent the first number is of the second number. This can be represented mathematically as:
\[ \text{Percentage} = \left( \frac{\text{First Number}}{\text{Second Number}} \right) \times 100 \]

Substituting the values we calculated:
\[ \text{Percentage} = \left( \frac{0.75x}{0.80x} \right) \times 100 \]

### Step 5: Simplify the Expression
The \( x \) in the numerator and denominator cancels out:
\[ \text{Percentage} = \left( \frac{0.75}{0.80} \right) \times 100 \]

### Step 6: Calculate the Fraction
Now, we can simplify \( \frac{0.75}{0.80} \):
\[ \frac{0.75}{0.80} = \frac{75}{80} = \frac{75 \div 5}{80 \div 5} = \frac{15}{16} \]

### Step 7: Convert to Percentage
Now we multiply by 100 to convert to percentage:
\[ \text{Percentage} = \frac{15}{16} \times 100 = 93.75 \]

### Conclusion
Thus, the first number is **93.75%** of the second number.

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