Two numbers are 40% and 80% less 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. 100
B. 33.3
C. 66.6
D. 200

Answer

To solve the problem step by step, let's define the numbers clearly and calculate the required percentage increase.

**Step 1: Define the third number.**
Let the third number be \( x \).

**Step 2: Calculate the first number.**
The first number is 40% less than the third number:
\[ \text{First number} = x - 0.4x = 0.6x \]

**Step 3: Calculate the second number.**
The second number is 80% less than the third number:
\[ \text{Second number} = x - 0.8x = 0.2x \]

**Step 4: Determine the difference between the first and second numbers.**
To find out how much the second number needs to be enhanced to equal the first number, we calculate the difference:
\[ \text{Difference} = \text{First number} - \text{Second number} = 0.6x - 0.2x = 0.4x \]

**Step 5: Calculate the percentage increase needed.**
To find the percentage increase required to make the second number equal to the first number, we use the formula:
\[ \text{Percentage Increase} = \left( \frac{\text{Difference}}{\text{Second number}} \right) \times 100 \]
Substituting the values:
\[ \text{Percentage Increase} = \left( \frac{0.4x}{0.2x} \right) \times 100 = \left( 2 \right) \times 100 = 200\% \]

Thus, the second number needs to be enhanced by **200%** to make it equal to the first number.

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