The average age of Rahul, Amit, Vijay and Salman is $ 4 q $ years old. Rahul is $ 2 q $ years old, Amit is $ q $ years old and Vijay is 14 years old. How old is Salman?
A. $ \quad(14 q) $ years
B. $ \quad(13 q) $ years
C. $ \quad(14 q-13) $ years
D. $ \quad(13 q-14) $ years
Given:
The average age of Rahul, Amit, Vijay and Salman is \( 4 q \) years old. Rahul is \( 2 q \) years old, Amit is \( q \) years old and Vijay is 14 years old.
To do:
We have to find the age of Salman.
Solution:
Let the age of Salman be $x$.
We know that,
Average $=$ Sum of the observations$\div$ Total number of observations.
Therefore, according to the question
$4q=\frac{2q+q+14+x}{4}$
$4(4q)=3q+14+x$ (On cross multiplication)
$16q=3q+14+x$
$x=16q-3q-14$
$x=13q-14$
The age of Salman is $(13q-14)$ years.
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