If A is 95% of B, then what percent of A is B?

The correct answer is $105\frac{5}{19}\%$.

We are told that A is 95% of B. We need to find what percent of A is B.

Step 1: Express A in terms of B.

Since A is 95% of B:

$A=\frac{95}{100}\times B$

Simplify the fraction:

$A=\frac{19}{20}\times B$

Step 2: Express B in terms of A.

Rearranging the equation above, we get:

$B=\frac{20}{19}\times A$

Step 3: Find what percent of A is B.

The required percentage is:

$\frac{B}{A}\times 100=\frac{20}{19}\times 100=\frac{2000}{19}$

Step 4: Convert the improper fraction to a mixed number.

Divide 2000 by 19:

19 × 105 = 1995, and 2000 - 1995 = 5

So:

$\frac{2000}{19}=105\frac{5}{19}$

Conclusion: B is $105\frac{5}{19}\%$ of A.

Key Insight: Since A is less than B (A is only 95% of B), it makes sense that B must be more than 100% of A — specifically, about 105.26% of A. This is a classic inverse percentage relationship: if A = (p/100) × B, then B = (100/p) × A × 100%.