`(2)/(3)rd` of first number is equal to the cube of the second number. If the second number is equal to `12%` of 100, what is sum of the first & `2^(nd)` number?

Options

A. A)2408
B. B)2640
C. C)2426
D. D)2604

Answer

To solve the problem step by step, we will follow the instructions provided in the question.

### Step 1: Understand the given information
We know that:
- Two-thirds of the first number (let's call it \( a \)) is equal to the cube of the second number (let's call it \( b \)).
- The second number \( b \) is equal to 12% of 100.

### Step 2: Calculate the value of the second number \( b \)
To find \( b \):
\[ b = 12\% \text{ of } 100 = \frac{12}{100} \times 100 = 12 \]

### Step 3: Set up the equation based on the relationship between \( a \) and \( b \)
According to the problem, we have:
\[ \frac{2}{3} a = b^3 \]
Substituting the value of \( b \):
\[ \frac{2}{3} a = 12^3 \]

### Step 4: Calculate \( 12^3 \)
Calculating the cube of 12:
\[ 12^3 = 12 \times 12 \times 12 = 144 \times 12 = 1728 \]

### Step 5: Substitute \( 12^3 \) back into the equation
Now we can rewrite the equation:
\[ \frac{2}{3} a = 1728 \]

### Step 6: Solve for \( a \)
To find \( a \), we will multiply both sides of the equation by \( \frac{3}{2} \):
\[ a = 1728 \times \frac{3}{2} \]
Calculating this gives:
\[ a = 1728 \times 1.5 = 2592 \]

### Step 7: Calculate the sum of the first and second numbers
Now we need to find the sum \( a + b \):
\[ a + b = 2592 + 12 = 2604 \]

### Final Answer
The sum of the first and second numbers is:
\[ \boxed{2604} \]

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