CAT 2018 Slot 2 — QA Question 10
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?
Answer & solution
1 : 3
- B
1 : 4
- C
2 : 5
- D
3 : 10
Suppose the concentrations of the solutions A, B and C are ‘a’, ‘b’ and ‘c’ respectively.
If the three solutions are mixed in the ratio 1 : 2 : 3, the resultant solution has 20% concentration. Therefore, we have
or a + 2b + 3c = 120 ...(1)
If the three solutions are mixed in the ratio 3 : 2 : 1, the resultant solution has 30% concentration. Therefore, we have
or 3a + 2b + c = 180 ...(2)
Multiplying equation (1) with 3 and (2) with 2 and equating both, we get
3a + 6b + 9c = 6a + 4b + 2c
⇒ 2b + 7c = 3a
Now, concentration of solution D = = =
Therefore the ratio of D's concentration to A's concentration
Hence, option (a).