The sum of the ages of Yogesh, Prakash and Sameer is 93 years. 10 years ago the ratio of their ages was 2 : 3 : 4. What is the present age of Sameer ?

Options

A. 32 years
B. 24 years
C. 34 years
D. None of these

Answer

To find the present age of Sameer, we can follow these steps:

### Step 1: Set up the equations based on the problem statement.
Let the present ages of Yogesh, Prakash, and Sameer be represented as:
- Yogesh's age = 2x
- Prakash's age = 3x
- Sameer's age = 4x

### Step 2: Write the equation for the sum of their ages.
According to the problem, the sum of their ages is 93 years:
\[ 2x + 3x + 4x = 93 \]

### Step 3: Simplify the equation.
Combine the terms on the left side:
\[ 9x = 93 \]

### Step 4: Solve for x.
To find the value of x, divide both sides by 9:
\[ x = \frac{93}{9} \]
\[ x = 10.33 \]

### Step 5: Calculate the present ages.
Now we can find the present ages of each person:
- Yogesh's age = 2x = 2 * 10.33 = 20.67 years
- Prakash's age = 3x = 3 * 10.33 = 31 years
- Sameer's age = 4x = 4 * 10.33 = 41.33 years

### Step 6: Round the ages to the nearest whole number.
Since ages are typically whole numbers, we round them:
- Yogesh's age ≈ 21 years
- Prakash's age ≈ 31 years
- Sameer's age ≈ 41 years

### Step 7: Verify the ages.
Check if the sum of the ages equals 93:
\[ 21 + 31 + 41 = 93 \]
This confirms that our calculations are correct.

### Step 8: Find the present age of Sameer.
Thus, the present age of Sameer is approximately:
\[ \text{Sameer's age} = 41 \text{ years} \]

### Final Answer:
The present age of Sameer is **41 years**.

---