Let `x_(1) lt x_(2) lt x_(3) lt x_(4) lt x_(5)` and `y_(1) lt y_(2) lt y_(3) lt y_(4) lt y_(5)` are in AP such that `underset(I = 1)overset(5)(sum) x_(i) = underset(I = 1)overset(5)(sum) y_(i) = 25` and `underset(I =1)overset(5)(II) x_(i) = underset(I = 1)overset(5)(II) y_(i) = 0` then `|y_(5) - x_(5)|`

Options

A. `5//2`
B. 5
C. 10
D. 15

Answer

B

Explanation

Let 5 nos in AP are
a - 2d, a -d, a,a + d, a + 2d
ATO `5a = 35 implies a = 5`
And `(a^(2) - 4d^(2)) (a^(2) - d^(2)) a = 0 implies d = (5)/(2)` or `d = 5`
So nos would be
`0,(5)/(2), 5, (15)/(2), 10` or -5,0,5,10,15