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CAT Previous Year Paper | CAT Ratio Proportions and Mixtures Questions | Question 33

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Question 33 : 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. 3 : 10
  2. 1 : 3
  3. 2 : 5
  4. 1 : 4

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Explanatory Answer

Method of solving this CAT Question from Ratio Proportions and Mixtures

Given that the strength of the salt solution is p% if 100 ml of the solution contains p grams of salt
It is also given that three salt solutions A , B , C are mixed in the proportion 1 : 2 : 3, then the resulting solution has strength 20%.
So \\frac{A + 2B + 3C}{6}) = 0.2 ⟹ A + 2B + 3C = 1.2 ------(1)
If instead the proportion is 3 : 2 : 1, then the resulting solution has strength 30%.
So, \\frac{3A + 2B + C}{6}) = 0.3 ⟹ 3A +2B + C = 1.8 -------(2)
It is given that 4th solution D is produced by mixing B and C in the ratio 2 : 7
So D = \\frac{2B + 7C}{9})
We have to find the ratio of the strength of D : A
Subtracting equations 1 and 2, we get
2A – 2C = 0.6 or A – C = 0.3
Since we could not find anything from the above methods, we can eliminate the number part and get the ratio going
A + 2B + 3C = 1.2
3A + 2B + C = 1.8
So let us multiply eqn 1 and 2 with 3 and 2,
3A + 6B + 9C = 6A + 4B + 2C
2B + 7C = 3A
It is given that D = \\frac{2B + 7C}{9})
\\frac{2B + 7C}{9}) = \\frac{3A}{9}) ⟹ \\frac{2B + 7C}{9}) = \\frac{A}{3})
Hence D = \\frac{A}{3})
Therefore the ratio D : A = 1 : 3

The question is "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"

Hence, the answer is 1 : 3

Choice B is the correct answer

 

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