Discussion

Explanation:

$\frac{a+b}{a-b}=\frac{5}{4}$

⇒ 4a+4b = 5a-5b

⇒  a = 9b

⇒ a/b = 9/1

⇒ a : b = 9 ∶ 1

Alternately, 

Apply Componendo & Dividendo, i.e.

If x/y = p/q, then (x+y)/(x-y) = (p+q)/(p-q)

Hence, (a+b)/(a-b) = 5/4

⇒ $\frac{(a+b)+(a-b)}{(a+b)-(a-b)}=\frac{5+4}{5-4}$

⇒ 2a/2b = 9/1

⇒ a/b = 9/1

Hence, option (a).

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