Question

he ratio of wages of a & b is 13:16. if A works for 9 days

Answer 1

Solution :-

Your question is incomplete. I think that you are asking about how many days will B work if A works for 9 days and the ratio of their respective wages is 13 : 16.

Here is the answer.

More wages, it means more number of days B have to work. It is the case of direct proportion. 

Let B works for x number of days.

⇒ 13 : 16 : 9 : x

⇒ 13x = 16*9

⇒ x = 144/13

⇒ x = 11.076  or 11 days (Approximately)

Answer.

Answer 2

Your question is incomplete. 
I guess that you are asking about the number of days for which B works if A works for 9 days provided that the ratio of their wages is 13:16
Let number of days for which B works = x = ?
More days ⇒ More wages
Less days ⇒ Less wages
So this is a question of direct proportion.
Hence,
13 : 16 :: 9 : x
(13) (x) = (16) (9)
13 x = 144
x = 144 / 13
x = 11
which shows that B works for 11 days.
Hopefully it helps. Thanks.