When 60% of a number is sub tracted from another number, the second number reduces to its 52%, the ratio of the first num ber to the second number is

Options

A. `6:5`
B. `5:3`
C. `5:4`
D. `4:5`

Answer

To solve the problem step by step, we will denote the first number as \( A \) and the second number as \( B \).

### Step 1: Understand the problem
The problem states that when 60% of the first number \( A \) is subtracted from the second number \( B \), the result is equal to 52% of the second number \( B \).

### Step 2: Set up the equation
From the problem, we can set up the equation:
\[ B - 0.6A = 0.52B \]

### Step 3: Rearrange the equation
To isolate \( A \), we can rearrange the equation:
\[ B - 0.52B = 0.6A \]
This simplifies to:
\[ 0.48B = 0.6A \]

### Step 4: Express \( A \) in terms of \( B \)
Now, we can express \( A \) in terms of \( B \):
\[ A = \frac{0.48B}{0.6} \]
To simplify this, we can multiply both the numerator and the denominator by 100 to eliminate the decimals:
\[ A = \frac{48B}{60} \]
Now, simplifying \( \frac{48}{60} \):
\[ A = \frac{4B}{5} \]

### Step 5: Find the ratio of \( A \) to \( B \)
Now we can find the ratio of \( A \) to \( B \):
\[ \frac{A}{B} = \frac{4B/5}{B} = \frac{4}{5} \]

### Step 6: Conclusion
Thus, the ratio of the first number \( A \) to the second number \( B \) is:
\[ \text{Ratio of } A \text{ to } B = 4:5 \]