The ratio of the ages of Riti and Nakul is 2:3. Eight years ago, the ratio of their ages was 2:5. Find! their present ages.

Answer

To solve the problem of finding the present ages of Riti and Nakul, we can follow these steps:

### Step 1: Define the variables based on the given ratio.
Let Riti's present age be represented as \(2x\) and Nakul's present age as \(3x\), based on the ratio of their ages, which is \(2:3\).

### Step 2: Express their ages 8 years ago.
Eight years ago, Riti's age would be \(2x - 8\) and Nakul's age would be \(3x - 8\).

### Step 3: Set up the equation based on the ratio 8 years ago.
According to the problem, the ratio of their ages 8 years ago was \(2:5\). Therefore, we can set up the equation:
\[ \frac{2x - 8}{3x - 8} = \frac{2}{5} \]

### Step 4: Cross-multiply to eliminate the fraction.
Cross-multiplying gives us:
\[ 5(2x - 8) = 2(3x - 8) \]

### Step 5: Expand both sides of the equation.
Expanding both sides results in:
\[ 10x - 40 = 6x - 16 \]

### Step 6: Rearrange the equation to isolate \(x\).
Now, we will move all terms involving \(x\) to one side and constant terms to the other side:
\[ 10x - 6x = 40 - 16 \]
This simplifies to:
\[ 4x = 24 \]

### Step 7: Solve for \(x\).
Dividing both sides by 4 gives:
\[ x = 6 \]

### Step 8: Calculate the present ages.
Now that we have \(x\), we can find the present ages:
- Riti's age: \(2x = 2 \times 6 = 12\) years
- Nakul's age: \(3x = 3 \times 6 = 18\) years

### Final Answer:
Riti's present age is 12 years, and Nakul's present age is 18 years.

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