The present age of Ram and Shyam is 34 years and 14 years respectively. After how many years Ram's age will be double of the Shyam's age ?

Question

Accepted Answer

To determine after how many years Ram's age will be double Shyam's age, we start with their current ages: Ram is 34 years old, and Shyam is 14 years old.

Let's denote the number of years after which Ram's age will be double Shyam's age as $ x $.

After $ x $ years:
- Ram's age will be $ 34 + x $.
- Shyam's age will be $ 14 + x $.

According to the problem, we need to find $ x $ such that:
$$ 34 + x = 2 \times (14 + x) $$

Solving this equation:
$$ 34 + x = 28 + 2x $$

Rearranging the terms gives:
$$ 34 - 28 = 2x - x $$
$$ 6 = x $$

Thus, after 6 years, Ram's age will be double Shyam's age. Therefore, Option 3 is correct.

Now, let's explain why the other options are incorrect:

1. **Option 1: 4 years**
   - After 4 years, Ram's age would be $ 34 + 4 = 38 $ and Shyam's age would be $ 14 + 4 = 18 $.
   - Double of Shyam's age would be $ 2 \times 18 = 36 $, which is not equal to Ram's age of 38.

2. **Option 2: 5 years**
   - After 5 years, Ram's age would be $ 34 + 5 = 39 $ and Shyam's age would be $ 14 + 5 = 19 $.
   - Double of Shyam's age would be $ 2 \times 19 = 38 $, which is not equal to Ram's age of 39.

3. **Option 4: 8 years**
   - After 8 years, Ram's age would be $ 34 + 8 = 42 $ and Shyam's age would be $ 14 + 8 = 22 $.
   - Double of Shyam's age would be $ 2 \times 22 = 44 $, which is not equal to Ram's age of 42.

Therefore, the only correct option is Option 3, which is 6 years.