48% of the 1st number is 60% of the 2nd number. What is the ratio of the 1st number to the 2nd number?

Options

A. `4:7`
B. `3:4`
C. `5:4`
D. Couldn't be determined

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the given information
The problem states that 48% of the first number is equal to 60% of the second number. We need to express this mathematically.

### Step 2: Set up the equation
Let the first number be \( x \) and the second number be \( y \). According to the problem, we can write:
\[ 0.48x = 0.60y \]

### Step 3: Eliminate the decimals
To simplify the equation, we can multiply both sides by 100 to eliminate the decimals:
\[ 48x = 60y \]

### Step 4: Rearrange the equation
Now, we can rearrange the equation to express it in terms of \( x \) and \( y \):
\[ \frac{x}{y} = \frac{60}{48} \]

### Step 5: Simplify the ratio
Now we simplify \( \frac{60}{48} \):
- Divide both the numerator and the denominator by 12:
\[ \frac{60 \div 12}{48 \div 12} = \frac{5}{4} \]

### Step 6: Write the ratio
Thus, the ratio of the first number to the second number is:
\[ x : y = 5 : 4 \]

### Final Answer
The ratio of the first number to the second number is \( 5 : 4 \).

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