If $a > b > c > 0,$ which of the following is always positive ?

(A) $(a-c)÷b$

(B) $b+c-a$

(C) $(c-b)×(a-b)$

(D) $(c-b) × (b-a)$

(E) $(a×b) - (a ×c)$

Choose the correct answer from the options given below :

(A), (D), (E) only

The correct answer is Option (3) → (A), (D), (E) only

$a > b > c > 0$ [given]

$⇒a-b>0;b-c>0;a-c>0$

(A) $(a-c)÷b$ will always be positive as both $(a-c)$ and $b$ is positive.

(D) $(c-b)<0, (b-a)<0$

$∴(c-b)(b-a)>0$   $[-1×-2=2]$ → Ex.

(E) $(a×b) - (a ×c)=a×(b-c)$

as both (A) and $(b-c)$ is positive the product will be also a positive.