Two numbers are less than a third number by `30%` and `37%` respectively. How much percent is the second number less than the first ?

Options

A. `3`
B. `7`
C. `10`
D. `4`

Answer

To solve the problem step by step, we need to find out how much percent the second number is less than the first number, given that the first number is 30% less than a third number and the second number is 37% less than the same third number.

### Step 1: Define the third number
Let the third number be represented as \( x \).

### Step 2: Calculate the first number
The first number is 30% less than the third number. Therefore, we can express the first number as:
\[ \text{First Number} = x - 0.30x = 0.70x \]

### Step 3: Calculate the second number
The second number is 37% less than the third number. We can express the second number as:
\[ \text{Second Number} = x - 0.37x = 0.63x \]

### Step 4: Find the difference between the first and second numbers
Now, we need to find the difference between the first and second numbers:
\[ \text{Difference} = \text{First Number} - \text{Second Number} = 0.70x - 0.63x = 0.07x \]

### Step 5: Calculate the percentage difference
To find out how much percent the second number is less than the first number, we use the formula:
\[ \text{Percentage Difference} = \left( \frac{\text{Difference}}{\text{First Number}} \right) \times 100 \]
Substituting the values we found:
\[ \text{Percentage Difference} = \left( \frac{0.07x}{0.70x} \right) \times 100 \]

### Step 6: Simplify the expression
The \( x \) cancels out:
\[ \text{Percentage Difference} = \left( \frac{0.07}{0.70} \right) \times 100 = \left( \frac{7}{70} \right) \times 100 = \left( \frac{1}{10} \right) \times 100 = 10\% \]

### Final Answer
The second number is **10%** less than the first number.

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