The sum of ages of 5 children born at the interval of 4 years each is 55 years, the age of eldest child is :

Question

Accepted Answer

To determine the age of the eldest child, we need to understand the distribution of ages among the five children. The children are born at intervals of 4 years, and the total sum of their ages is 55 years.

Let's denote the age of the youngest child as $ x $. Therefore, the ages of the children can be expressed as follows:
- Youngest child: $ x $
- Second child: $ x + 4 $
- Third child: $ x + 8 $
- Fourth child: $ x + 12 $
- Eldest child: $ x + 16 $

The sum of their ages is given by:
$$ x + (x + 4) + (x + 8) + (x + 12) + (x + 16) = 55 $$

Simplifying the equation:
$$ 5x + 40 = 55 $$

Subtract 40 from both sides:
$$ 5x = 15 $$

Divide by 5:
$$ x = 3 $$

Thus, the age of the eldest child is:
$$ x + 16 = 3 + 16 = 19 $$

Therefore, the age of the eldest child is 19 years, which corresponds to Option 4.

**Explanation for why other options are incorrect:**

1. **Option 1 (15 years):** If the eldest child were 15 years old, the ages would be $ x, x+4, x+8, x+12, 15 $. Solving for $ x $ would not satisfy the total sum of 55 years.

2. **Option 2 (21 years):** If the eldest child were 21 years old, the ages would be $ x, x+4, x+8, x+12, 21 $. Solving for $ x $ would result in a total sum greater than 55 years.

3. **Option 3 (16 years):** If the eldest child were 16 years old, the ages would be $ x, x+4, x+8, x+12, 16 $. Solving for $ x $ would not satisfy the total sum of 55 years.

In conclusion, the only option that satisfies the conditions given in the problem is Option 4, where the age of the eldest child is 19 years.