Question

Median of the data a/3,a/2,a/4,2a/5,a/6 is 12 if a is positive find the value of a

Answer 1

1. First arrange them in increasing order.

LCM of denominators = 60
a/3 = (a×20)/(3×20) = 20a/60
a/2 = (a×30)/(2×30) = 30a/60
a/4 = (a×15)/(4×15) = 15a/60
2a/5 = (2a×12)/(5×12) = 24a/60
a/6 = (a×10)/(6×10) = 10a/60

In the increasing order =  a/6, a/4, a/3, 2a/5, a/2
so median is the third term = a/3
given that median is 12
So a/3 = 12
⇒ a = 12×3
⇒ a = 36