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Three bags whose volumes are in the ratio 3:5:7 are full of lime and silica. In the first bag, the ratio of lime and silica is 5:1; in the second bag, the ratio is 7:3; and in the third bag, the ratio is 3:4. All three mixtures are mixed in another bag. Find the ratio of lime and silica in the final mixture.
- 4:3
- 3:2
- 3:4
- 2:3
Correct answer: 3:2
Solution
Let the bag volumes be 3x, 5x, and 7x. Lime and silica in the three bags are: first bag 5/6 and 1/6 of 3x, second bag 7/10 and 3/10 of 5x, third bag 3/7 and 4/7 of 7x. Adding gives total lime = 2.5x + 3.5x + 3x = 9x and total silica = 0.5x + 1.5x + 4x = 6x, so the ratio is 9:6 = 3:2.
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