Two numbers are 40% and 35% lesser than a third number. By how much percent is the first number to be enhanced to make it equal to the second number?

Options

A. (a) `8 1/3%`
B. (b) `12 1/2%`
C. (c) `13 1/3%`
D. (d) `6 1/4%`

Answer

To solve the problem step by step, we need to find out how much the first number (A) needs to be increased to make it equal to the second number (B).

### Step 1: Define the third number
Let's denote the third number as \( C \). For simplicity, we can assume \( C = 100 \).

### Step 2: Calculate the first number (A)
The first number is 40% less than the third number.
\[ A = C - 40\% \text{ of } C = 100 - 40 = 60 \]

### Step 3: Calculate the second number (B)
The second number is 35% less than the third number.
\[ B = C - 35\% \text{ of } C = 100 - 35 = 65 \]

### Step 4: Find the difference between B and A
Now, we need to find the difference between the second number (B) and the first number (A).
\[ B - A = 65 - 60 = 5 \]

### Step 5: Calculate the percentage increase needed for A to equal B
To find out by what percentage A needs to be increased to become equal to B, we use the formula for percentage increase:
\[ \text{Percentage Increase} = \left( \frac{B - A}{A} \right) \times 100 \]
Substituting the values we found:
\[ \text{Percentage Increase} = \left( \frac{5}{60} \right) \times 100 \]

### Step 6: Simplify the calculation
Calculating the above expression:
\[ \text{Percentage Increase} = \frac{5 \times 100}{60} = \frac{500}{60} = \frac{25}{3} \approx 8.33\% \]

### Final Answer
Thus, the first number needs to be enhanced by \( \frac{25}{3} \) percent or \( 8 \frac{1}{3} \) percent to make it equal to the second number.

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