Question

The strength of a salt solution is p% if 100 ml of the solution contains p grams of salt. If three salt solutions A, B, C are mixed in the proportion 1 : 2 : 3, then the resulting solution has strength 20%. If instead the proportion is 3 : 2 : 1, then the resulting solution has strength 30%. A fourth solution, D, is produced by mixing B and C in the ratio 2 : 7. The ratio of the strength of D to that of A is

• A. 2:5
• B. 1:3
• C. 1:4
• D. 3:10

Answer 1

Answer: (B)

1:3

Answer 2

The correct answer is (B):
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%.
⇒ a+2b+3c/1+2+3 = 20
⇒ a+2b+3c = 120...(1)
Also, if the proportion is 3 : 2 : 1, then the resulting Solution has strength 30%.
⇒ 3a+2b+c/1+2+3 = 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 = 15/45 = 1:3.