Calculating Eldest Person's Age from Average and Ratio

The problem involves finding the age of the eldest person given the average age of three people and the ratio of their ages.

Step 1: Calculate the Total Age

The average age of 3 persons is 30 years. The total age is calculated by multiplying the average age by the number of persons.

Total Age = Average Age $\times$ Number of Persons

Total Age = 30 years $\times$ 3 = 90 \text{ years}

Step 2: Represent Ages Using the Ratio

The ages are in the ratio 3 : 5 : 7. Let the common multiplier be '$x$'. Therefore, the ages can be represented as $3x$, $5x$, and $7x$ years.

Step 3: Formulate and Solve the Equation

The sum of the individual ages must equal the total age calculated in Step 1.

Sum of Ages = $3x + 5x + 7x$

Set the sum equal to the total age:

$3x + 5x + 7x = 90$

$15x = 90$

Solve for '$x$':

$x = \frac{90}{15}

$x = 6$

Step 4: Determine the Eldest Person's Age

The eldest person corresponds to the largest part of the ratio, which is $7x$. Substitute the value of '$x$' found in Step 3.

Eldest Person's Age = $7x$

Eldest Person's Age = $7 \times 6$

Eldest Person's Age = 42 \text{ years}