The mean age of three students Vijay, Rahul and Anu is 15 years. If there are in the ratio 4: 5: 6 respectively, their ages are:

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12 years, 15 years, 18 years

12 years, 18 years, 15 years

18 years, 15 years, 12 years

15 years, 12 years, 18 years

answer is A.

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Detailed Solution

Given,
Total students = 3
The mean age of three students Vijay, Rahul and Anu = 15 year.
Age ratio of the students = 4:5:6
Suppose the age of Vijay, Rahul and Anu to be x, y and z years.
Now we know that,

mean = \frac{sum of observations}{total observation} \Rightarrow \frac{x + y + z}{3} = 15

\Rightarrow x + y + z = 45

So, sum of the ages = 45.
Therefore,
Vijay’s age

x = \frac{4}{4 + 5 + 6} \times

(Sum of ages)

\Rightarrow x = \frac{4}{15} \times (45)

\Rightarrow x = 4 \times (3)

\Rightarrow x = 12

years
Rahul’s age,

\Rightarrow y = \frac{5}{15} \times 45

\Rightarrow y = 5 \times 3

\Rightarrow y = 15 Years

Anu’s age,

\Rightarrow z = \frac{6}{15} \times (45)

\Rightarrow z = 6 \times (3)

\Rightarrow z = 18 Years

So,
Age of Vijay 12 years
Age of Rahul 15 years
Age of Anu 18 years
Option 1 is correct.

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