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
1. 1 : 4
2. 3 : 10
3. 1 : 3
4. 2 : 5

Answer 1

Correct Answer - Option 3 : 1 : 3

Calculation:

Let 'p', 'q' and 'r' 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%.
⇒ (p + 2q + 3r)/(1 + 2 + 3) = 20

⇒ p + 2q + 3r = 120     …….(1)
Also, if the proportion is 3 : 2 : 1, then the resulting Solution has a strength 30%.
⇒ (3p + 2q + r)/(3 + 2 + 1) = 30  

⇒ 3p + 2q + r = 180     ………..(2)
From equation (1) and (2), we get
⇒ q + 2r = 45
By observation, we find that q = r = 15 and p = 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