If `60%` of `A=(3)/(4)` of B , then A:B is

Options

A. `9:20`
B. `20:9`
C. `4:5`
D. `5:4`

Answer

To solve the problem, we need to find the ratio A:B given that 60% of A is equal to (3/4) of B. Let's break it down step by step.

### Step 1: Write the equation based on the problem statement
We know that:
\[ 60\% \text{ of } A = \frac{3}{4} \text{ of } B \]

This can be expressed mathematically as:
\[ \frac{60}{100} \times A = \frac{3}{4} \times B \]

### Step 2: Simplify the percentage
We can simplify \( 60\% \) as:
\[ \frac{60}{100} = \frac{3}{5} \]
So, we can rewrite the equation as:
\[ \frac{3}{5} A = \frac{3}{4} B \]

### Step 3: Cross-multiply to eliminate the fractions
To eliminate the fractions, we can cross-multiply:
\[ 3 \times 4 A = 3 \times 5 B \]
This simplifies to:
\[ 12A = 15B \]

### Step 4: Rearrange the equation to find the ratio
Now, we can rearrange the equation to find the ratio of A to B:
\[ \frac{A}{B} = \frac{15}{12} \]

### Step 5: Simplify the ratio
We can simplify \( \frac{15}{12} \) by dividing both the numerator and the denominator by their greatest common divisor, which is 3:
\[ \frac{A}{B} = \frac{15 \div 3}{12 \div 3} = \frac{5}{4} \]

### Step 6: Write the final ratio
Thus, the ratio of A to B is:
\[ A : B = 5 : 4 \]

### Final Answer
The ratio A:B is \( 5:4 \).

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