If A is `20%` more than C and B is `60%`1 more than C, then A' is what percentage of B?

Answer

To solve the problem step by step, we will find the values of A and B in terms of C, and then determine what percentage A is of B.

### Step 1: Find the value of A in terms of C
Given that A is 20% more than C, we can express this mathematically as:
\[ A = C + 20\% \text{ of } C \]
This can be rewritten as:
\[ A = C + \frac{20}{100}C \]
Combining the terms gives:
\[ A = C + 0.2C = 1.2C \]

### Step 2: Find the value of B in terms of C
Next, we know that B is 60% more than C. We can express this as:
\[ B = C + 60\% \text{ of } C \]
This can be rewritten as:
\[ B = C + \frac{60}{100}C \]
Combining the terms gives:
\[ B = C + 0.6C = 1.6C \]

### Step 3: Determine A as a percentage of B
Now, we want to find what percentage A is of B. We can set up the equation:
\[ \frac{A}{B} = \frac{1.2C}{1.6C} \]
Since C is common in both the numerator and the denominator, we can cancel it out:
\[ \frac{A}{B} = \frac{1.2}{1.6} \]

### Step 4: Simplify the fraction
To simplify \(\frac{1.2}{1.6}\), we can multiply both the numerator and the denominator by 10 to eliminate the decimal:
\[ \frac{1.2 \times 10}{1.6 \times 10} = \frac{12}{16} \]
Now, we can simplify \(\frac{12}{16}\) by dividing both the numerator and the denominator by 4:
\[ \frac{12 \div 4}{16 \div 4} = \frac{3}{4} \]

### Step 5: Convert the fraction to a percentage
To find out what percentage \(\frac{3}{4}\) is, we multiply by 100:
\[ \frac{3}{4} \times 100 = 75\% \]

### Conclusion
Thus, A is 75% of B.