Three mixtures containing water and milk in ratios of 2:3, 4:5 and 3:4

Question

Three mixtures containing water and milk in ratios of 2:3, 4:5 and 3:4 are mixed in a proportion of 5:9:14. Find the fraction of the resulting mixture that needs to be replaced with milk for this mixture to contain 75 per cent milk.

A. 37/72
B. 12/19
C. 5/12
D. 53/112
E. 19/76

A. 37/72
B. 12/19
C. 5/12
D. 53/112
E. 19/76

chetan2u · Accepted Answer

Let the three mix be 5, 9 and 14 liters respectively for mixtures containing water and milk in ratios of 2:3, 4:5 and 3:4, then milk will be  5*\frac{3}{5} + 9*\frac{5}{9} + 14*\frac{4}{7} = 3+5+8 = 16 .

So, 16 out of 5+9+14 or 28 liters is milk. But we require milk to be 75% of 28 or 21 liters.

So we have to replace 5 liters of water by milk as whatever is the proportion of milk that is removed is filled back by milk.
Thus, 5/12 of mixture would mean 5/12 of water + 5/12 of milk.

HarshavardhanR · Answer

https://gmatclub.com/forum/download/file.php?id=82468 ___ Harsha Enthu about all things GMAT | Exploring the GMAT space | My website: gmatanchor.com GMAT-Club-Forum-9q5ltip8.png

ayushikamal001 · Answer

where did we get 16+x-(4/7)x from? GMAT-Club-Forum-p9yxn4bh.png

HarshavardhanR · Answer

Hi ayushikamal001 , Look at the bottom 4 rows of the "Milk" column. -> By mixing the 3 mixtures at 5:9:14 ratio, we arrived at a mix (28 units total) which has 16 units of milk . -> Now, from the mix (28 units), a quantity x was removed . -> How much milk was removed as a result of x units of the mix being removed? -> (16/28)x . -> Now, x quantity of milk is added . In effect, the final quantity of milk in the final mix will be 16 ( original amount of milk) - (16/28)x (quantity of milk removed when x units of mix got removed) + x (quantity of milk added as replacement). We know this final quantity to be 21 units (75% of 28). So, 16 - (16/28)x + x = 21. Hope this helps! ___ Harsha Enthu about all things GMAT | Exploring the GMAT space | My website: gmatanchor.com GMAT-Club-Forum-0g659en0.png

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Three mixtures containing water and milk in ratios of 2:3, 4:5 and 3:4

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Three mixtures containing water and milk in ratios of 2:3, 4:5 and 3:4

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