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Thestrength 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?
Verified Answer
Thestrength of a salt solution is p% if 100 ml of the solution contai...
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)
If instead the proportion is 3 : 2 :1, then the resulting solution has strength 30%.
=> 3a + 2b + 3c/1+2+3 = 30
=>3a + 2b + c = 180 ... (2)
From equation (1) and (2), we can say that
=> b + 2c = 45
=> b = 45 – 2c
Also, on subtracting (1) from (2), we get
a - c = 30
=> a = 30 + c
In solution D, B and C are mixed in the ratio 2:7
So, the concentration of salt in D = 2b + 7c/9 = 90 - 4c + 7c /9 = 90 + 3c/9
Required ratio = 90 + 3c/9a = 90 + 3c/9(30+c) = 1 : 3
Hence, option B is the correct answer.
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Most Upvoted Answer
Thestrength of a salt solution is p% if 100 ml of the solution contai...
Given Information:
- Strength of a salt solution is p% if 100 ml of the solution contains p grams of salt.
- Solution A has strength 20% when mixed in the proportion 1:2:3.
- Solution B has strength 30% when mixed in the proportion 3:2:1.
- Solution D is produced by mixing B and C in the ratio 2:7.

Calculating the strength of each solution:
- Let the strengths of solutions A, B, and C be a%, b%, and c% respectively.
- According to the given information, the resulting solution when mixed in the proportions 1:2:3 has a strength of 20%. This implies:
a/6 + 2b/6 + 3c/6 = 20
a/6 + b/3 + c/2 = 20
3a + 2b + 3c = 120 ... (1)
- Similarly, when mixed in the proportions 3:2:1, the resulting solution has a strength of 30%. This implies:
3a/6 + 2b/6 + c/6 = 30
a/2 + b/3 + c/6 = 30
3a + 2b + c = 180 ... (2)
- Given that solution D is produced by mixing B and C in the ratio 2:7, the strength of D is:
(2b + 7c) / (2 + 7) = (2b + 7c) / 9
= 2b/9 + 7c/9

Ratio of strengths of D to A:
- From equations (1) and (2), we have:
3a + 2b + 3c = 120
3a + 2b + c = 180
- Subtracting the first equation from the second:
c = 60
- Substituting c = 60 in the strength of D:
2b/9 + 7(60)/9
= 2b/9 + 420/9
= (2b + 420) / 9
- The ratio of the strength of D to A is:
(2b + 420) / 9 : 120/6
= (2b + 420) / 9 : 20
= b/4 + 70/3 : 20
= b/4 : 20 - 70/3
= b/4 : 50/3
= b : 50/12
= b : 4.17
Therefore, the ratio of the strength of D to that of A is 1:3.
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Thestrength 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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