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Author:  Bunuel [ 08 Apr 2020, 10:42 ] 
Post subject:  The strength of a salt solution is p% if 100 ml of the solution contai 
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. What is the ratio of the strength of D to that of A ? A. 3 : 10 B. 1 : 3 C. 2 : 5 D. 1 : 4 E. 1 : 5 Are You Up For the Challenge: 700 Level Questions 
Author:  smyarga [ 08 Apr 2020, 11:12 ] 
Post subject:  Re: The strength of a salt solution is p% if 100 ml of the solution contai 
Let three salt solutions A, B, C have the strengths p%, q%, r% respectively. Using weights from ratio 1:2:3 we will have the equation \(\frac{p}{6}+\frac{2q}{6}+\frac{3r}{6}=20\) or \(p+2q+3r=120\) Using weights from ration 3:2:1 we have the next equation \(\frac{3p}{6}+\frac{2q}{6}+\frac{r}{6}=30\) or \(3p+2q+r=180\) If we subtract first equation from the second one, we obtain: 2p2r=60 or r=p30. If we put it in the second equation, we get 3p+2q+p30=180 or 2q=2104p or q=1052p The question is to find the ratio: \((\frac{2q}{9}+\frac{7r}{9}):p=(2104p+7p210):9p=3p:9p=1:3\) The correct answer is B. 
Author:  Kinshook [ 10 Apr 2020, 09:30 ] 
Post subject:  Re: The strength of a salt solution is p% if 100 ml of the solution contai 
Bunuel wrote: 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. What is the ratio of the strength of D to that of A ? A. 3 : 10 B. 1 : 3 C. 2 : 5 D. 1 : 4 E. 1 : 5 Are You Up For the Challenge: 700 Level Questions Given: 1. The strength of a salt solution is p% if 100 ml of the solution contains p grams of salt. 2. If three salt solutions A, B, C are mixed in the proportion 1 : 2 : 3, then the resulting solution has strength 20%. 3. If instead the proportion is 3 : 2 : 1, then the resulting solution has strength 30%. 4. A fourth solution, D, is produced by mixing B and C in the ratio 2 : 7. Asked: What is the ratio of the strength of D to that of A ? Let the strength of solutions A, B & C be x%, y% & z% respectively 2. If three salt solutions A, B, C are mixed in the proportion 1 : 2 : 3, then the resulting solution has strength 20%. (x + 2y + 3z) / 6 = 20 x + 2y + 3z = 120 (1) 3. If instead the proportion is 3 : 2 : 1, then the resulting solution has strength 30%. 3x + 2y + z = 180 (2) (1) + (2) 4x + 4y + 4z = 300 x + y + z = 75 (3) 2*(3)  (1) x  z = 30 x = z + 30 z = x  30 (5) y = 75  x  z = 75  x  (x30) = 105  2x (6) 4. A fourth solution, D, is produced by mixing B and C in the ratio 2 : 7. Strength of D = (2y +7z)/9 The ratio of the strength of D to that of A = (2y + 7z)/9x = {2(105 2x) +7(x30)} / 9x = (210  4x + 7x  210 )/9x = 3x/9x = 1/3 IMO B 
Author:  bumpbot [ 19 Jan 2023, 03:40 ] 
Post subject:  Re: The strength of a salt solution is p% if 100 ml of the solution contai 
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