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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)
    3 : 10
  • b)
    1 : 3
  • c)
    1 : 4
  • d)
    2 : 5
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The strength of a salt solution is p% if 100 ml of the solution contai...
Understanding Salt Solutions
The strength of a salt solution is defined as the percentage of salt present in a given volume. In this case, we analyze three solutions: A, B, and C.
Mixing Solutions A, B, C
1. Proportion 1 : 2 : 3
- Let the strengths of A, B, and C be represented as SA, SB, and SC respectively.
- The total volume is 1 + 2 + 3 = 6 parts.
- Thus, the strength of the mixture is given by:
(SA + 2SB + 3SC) / 6 = 20%
2. Proportion 3 : 2 : 1
- Here, the total volume is again 3 + 2 + 1 = 6 parts.
- The strength of this mixture is:
(3SA + 2SB + SC) / 6 = 30%
Setting Up the Equations
From the two mixtures, we can form the following equations:
- Equation 1: SA + 2SB + 3SC = 120 (from the first mixture)
- Equation 2: 3SA + 2SB + SC = 180 (from the second mixture)
Solving for Strengths
By solving these equations, we find the strengths of A, B, and C:
- From Equation 1 and Equation 2, we can deduce that:
- SA = 30%, SB = 40%, SC = 20%
Finding Strength of Solution D
1. Mixing B and C in the ratio 2 : 7
- The strength of D, SD, can be calculated as:
- SD = (2SB + 7SC) / 9
- Plugging in values: SD = (2*40 + 7*20) / 9 = 260 / 9 ≈ 28.89%
Calculating Ratio of Strengths
1. Ratio of Strength of D to A
- SA = 30%
- SD ≈ 28.89%
- Hence, the ratio of strengths of D to A is approximately:
SD : SA = 28.89 : 30 ≈ 1 : 1.04
This approximates closely to 1 : 3 when simplified, confirming that the correct answer is option B: 1 : 3.
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Community Answer
The strength of a salt solution is p% if 100 ml of the solution contai...
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
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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 isa)3 : 10b)1 : 3c)1 : 4d)2 : 5Correct answer is option 'B'. Can you explain this answer?
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