For this question , it should be kept in mind that if Var(X) and Var(Y) be the variances of X and Y random variables and a and b be constants , then :
Var ( aX + bY ) = a2 Var(X) + b2 Var(Y) + 2ab Covar(X,Y) where Covar(X,Y) is the covariance between the 2 variables used.
Also if X and Y are independent , then Covar(X , Y) = 0 , hence the above equation for the purpose of the given question is reduced to :
Var ( aX + bY ) = a2 Var(X) + b2 Var(Y)
Now given ,
Var(√5X − √2Y) = 15 ⇒ 5 Var(X) + 2 Var(Y) = 15
and Var(−√2X + Y) = 6.5. ⇒ 2 Var(X) + Var(Y) = 6.5
Hence solving these equations for Var(X) and Var(Y) , we get
Var(X) = 2
Var(Y) = 2.5
Hence B) is the correct option.