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CAT 2018 Question Paper | Quants Slot 2

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

Do you feel that questions from the topic of Mixtures are the worst nightmares that you could ever go through? Conquer this fear by incorporating the strategy of practicingCAT Previous Year Paper in your Online CAT Preparation. Try this problem from CAT 2018 Question Paper and see if you can get to the answer before watching the video explanation.

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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