`45%` of first number is equal to `60%` of second number. If average of both the numbers is 10 less than the first number, then find `80%` of second number?

Options

A. A)64
B. B)40
C. C)48
D. D)56

Answer

To solve the problem step by step, we will follow the instructions given in the video transcript and break it down clearly.

### Step 1: Set up the equations
Let the first number be \( A \) and the second number be \( B \). According to the problem, we have:
\[ 0.45A = 0.60B \]

### Step 2: Simplify the equation
To find the ratio of \( A \) to \( B \), we can rearrange the equation:
\[ \frac{A}{B} = \frac{0.60}{0.45} \]
Dividing both the numerator and denominator by \( 0.15 \):
\[ \frac{A}{B} = \frac{60/15}{45/15} = \frac{4}{3} \]
This means:
\[ A : B = 4 : 3 \]

### Step 3: Express \( A \) and \( B \) in terms of a variable
Let’s assume \( A = 4x \) and \( B = 3x \) for some variable \( x \).

### Step 4: Find the average of \( A \) and \( B \)
The average of \( A \) and \( B \) is given by:
\[ \text{Average} = \frac{A + B}{2} = \frac{4x + 3x}{2} = \frac{7x}{2} \]

### Step 5: Set up the equation based on the average
According to the problem, the average is 10 less than the first number \( A \):
\[ \frac{7x}{2} = 4x - 10 \]

### Step 6: Solve for \( x \)
To eliminate the fraction, multiply the entire equation by 2:
\[ 7x = 8x - 20 \]
Rearranging gives:
\[ 20 = 8x - 7x \]
Thus:
\[ x = 20 \]

### Step 7: Find the values of \( A \) and \( B \)
Now substitute \( x \) back into the expressions for \( A \) and \( B \):
\[ A = 4x = 4 \times 20 = 80 \]
\[ B = 3x = 3 \times 20 = 60 \]

### Step 8: Calculate \( 80\% \) of \( B \)
Now, we need to find \( 80\% \) of \( B \):
\[ 80\% \text{ of } B = 0.80 \times 60 = \frac{80}{100} \times 60 = \frac{4800}{100} = 48 \]

### Final Answer
Thus, \( 80\% \) of the second number \( B \) is:
\[ \boxed{48} \]