The average age of 3 persons is 30 years.If their ages are in the ratio of 3 : 5 : 7 respectively, then the age of the eldest person is:
42 Years
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}
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