Let 'a', 'b' and 'c' be the concentration of salt in Solutions A, B and C respectively.
It is given that three salt solutions
A,B,C are mixed in the proportion
1:2:3, then the resulting Solution has strength
20%.
⇒‌=20 ⇒a+2b+3c=120.....(1)
Also, if the proportion is
3:2:1, then the resulting Solution has strength
30%.
⇒‌=30 ⇒3a+2b+c=180.....(2)
From equation (1) and (2), we get
⇒b+2c=45 By observation, we find that
b=c=15 and
a=45.
So if we mix Solution
B and
C in any ratio we get the mixture with
15% concentration whereas
A's strength
=45%.
Hence, the required ratio
=‌=1:3