Two numbers are in the ratio 5 : 6. If 8 is subtracted from each of the numbers, the ratio becomes 4 : 5, then find the numbers.

Options

A. `x= 42, y= 44`
B. `x= 48, y=40`
C. `x=40, y=48`
D. `x= 50 , y=40`

Explanation

To solve the problem, we will follow these steps:

### Step 1: Define the Variables
Let the two numbers be represented as:
- First number = 5x
- Second number = 6x

### Step 2: Set Up the Equation
According to the problem, if we subtract 8 from each number, the new ratio becomes 4:5. We can express this as:
\[ \frac{5x - 8}{6x - 8} = \frac{4}{5} \]

### Step 3: Cross Multiply
To eliminate the fraction, we will cross-multiply:
\[ 5(5x - 8) = 4(6x - 8) \]

### Step 4: Distribute
Now, we will distribute both sides:
\[ 25x - 40 = 24x - 32 \]

### Step 5: Rearrange the Equation
Next, we will rearrange the equation to isolate x:
\[ 25x - 24x = -32 + 40 \]
\[ x = 8 \]

### Step 6: Find the Numbers
Now that we have the value of x, we can find the two numbers:
- First number = 5x = 5(8) = 40
- Second number = 6x = 6(8) = 48

### Conclusion
The two numbers are 40 and 48.

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