If the median and the range of four numbers {x,y,2x+y,x−y} where 0<x<y are 10 and 32 respectively, then the mean of the numbers is
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Solution
Given x<y⇒x−y<0 Now, arranging given number's in increasing order x−y<x<y<2x+y ∴Range =(2x+y)−(x−y)=32 ⇒x+2y=32⋯(1) and median =y+x2=10 ⇒x+y=20⋯(2) solving equation (1) and (2) x=8,y=12 ∴ mean =x−y+y+x+2x+y4=x+y4 ∴ mean =11