The average ages of three persons is 27 years. Their ages are in the proportion of 1:3:5.What is the age in years of the youngest one among them
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Correct Answer: Option B
Explanation:
To solve this problem, follow these steps:
1. Find the total sum of the ages:
The average age of the three persons is 27 years. Since there are three persons, the total sum of their ages is:
\[
\text{Total sum} = \text{Average} \times \text{Number of persons} = 27 \times 3 = 81
\]
2. Use the given ratio to find the individual ages:
The ages are in the ratio 1:3:5. Let the ages be \( x \), \( 3x \), and \( 5x \). The sum of these ages should equal the total sum we calculated:
\[
x + 3x + 5x = 81
\]
Simplify to find \( x \):
\[
9x = 81
\]
\[
x = \frac{81}{9} = 9
\]
3. Find the age of the youngest person:
The youngest person’s age is \( x \), which is:
\[
x = 9
\]
Thus, the age of the youngest person is 9 years, which corresponds to option B.
To solve this problem, follow these steps:
1. Find the total sum of the ages:
The average age of the three persons is 27 years. Since there are three persons, the total sum of their ages is:
\[
\text{Total sum} = \text{Average} \times \text{Number of persons} = 27 \times 3 = 81
\]
2. Use the given ratio to find the individual ages:
The ages are in the ratio 1:3:5. Let the ages be \( x \), \( 3x \), and \( 5x \). The sum of these ages should equal the total sum we calculated:
\[
x + 3x + 5x = 81
\]
Simplify to find \( x \):
\[
9x = 81
\]
\[
x = \frac{81}{9} = 9
\]
3. Find the age of the youngest person:
The youngest person’s age is \( x \), which is:
\[
x = 9
\]
Thus, the age of the youngest person is 9 years, which corresponds to option B.