If 15 % of (A+B) = 25 % of (A-B( , then twhat per cent of B is equal to A ?

Options

A. 0.1
B. 0.6
C. 2
D. 4

Answer

To solve the equation given in the question, we start with the expression:

\[ 15\% \text{ of } (A + B) = 25\% \text{ of } (A - B) \]

We can express the percentages as fractions:

\[ \frac{15}{100} (A + B) = \frac{25}{100} (A - B) \]

Now, we can simplify the fractions:

\[ \frac{3}{20} (A + B) = \frac{1}{4} (A - B) \]

Next, we can eliminate the fractions by multiplying both sides by 20 (the least common multiple of the denominators):

\[ 3(A + B) = 5(A - B) \]

Now, we will distribute both sides:

\[ 3A + 3B = 5A - 5B \]

Next, we will rearrange the equation to isolate terms involving \(A\) and \(B\):

\[ 3A + 3B + 5B = 5A \]

This simplifies to:

\[ 3A + 8B = 5A \]

Now, we will move \(3A\) to the right side:

\[ 8B = 5A - 3A \]

This simplifies to:

\[ 8B = 2A \]

Now, we can solve for \(A\) in terms of \(B\):

\[ A = 4B \]

To find what percent of \(B\) is equal to \(A\), we can express \(A\) as a percentage of \(B\):

\[ \frac{A}{B} \times 100 = \frac{4B}{B} \times 100 = 4 \times 100 = 400\% \]

Thus, \(A\) is equal to 400% of \(B\).

### Summary of Steps:
1. Write the equation based on the given percentages.
2. Convert percentages to fractions.
3. Eliminate fractions by multiplying through by a common denominator.
4. Distribute and rearrange terms to isolate \(A\) and \(B\).
5. Solve for \(A\) in terms of \(B\).
6. Convert \(A\) to a percentage of \(B\).