The persent ages of A and B are as `6 : 4`. Five years ago their ages were in the ratio `5 :3` Find their present ages.

Options

A. 42, 28
B. 36, 24
C. 30, 20
D. 25, 15

Answer

To find the present ages of A and B given their age ratios, we can follow these steps:

### Step 1: Set up the equations based on the given ratios
Let the present ages of A and B be represented as:
- Age of A = 6x
- Age of B = 4x

### Step 2: Establish the equation for their ages 5 years ago
Five years ago, their ages would be:
- Age of A 5 years ago = 6x - 5
- Age of B 5 years ago = 4x - 5

According to the problem, five years ago their ages were in the ratio of 5:3. Therefore, we can set up the equation:
\[ \frac{6x - 5}{4x - 5} = \frac{5}{3} \]

### Step 3: Cross-multiply to eliminate the fraction
Cross-multiplying gives us:
\[ 3(6x - 5) = 5(4x - 5) \]

### Step 4: Expand both sides of the equation
Expanding both sides:
\[ 18x - 15 = 20x - 25 \]

### Step 5: Rearrange the equation to isolate x
Rearranging the equation:
\[ 18x - 20x = -25 + 15 \]
\[ -2x = -10 \]

### Step 6: Solve for x
Dividing both sides by -2:
\[ x = 5 \]

### Step 7: Calculate the present ages of A and B
Now that we have the value of x, we can find the present ages:
- Age of A = 6x = 6 * 5 = 30 years
- Age of B = 4x = 4 * 5 = 20 years

### Final Answer
The present ages of A and B are:
- Age of A = 30 years
- Age of B = 20 years

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