Multiple choice

Directions : Answer the question independently. Two identical samples of 225 ml of a composite liquid M, which is a mixture of liquids A, B and water, were sent to two testing labs P and Q to determine the ratio in which A, B and water are present in M. While transporting the 225ml sample to lab P, some water accidently seeped into the sample and the lab gave the test results as 2:3:5. While transporting the other sample to lab Q, some water got evaporated and the test results came out to be 6:9:10. If the amount of water that got added in the first sample is four times the amount of water that got evaporated in the second sample, find the ratio in which the three liquids A, B and water are present in M.

  1. 2:3:15

  2. 8:12:15

  3. 12:18:25

  4. 6:9:11

  5. Culture influences choice making. Individualistic societies are taught the importance of personal choice while collectivist societies emphasize that what you eat, what you play with, what you study etc should be determined by society and should not be left to the whims of the individual.
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D Correct answer
Explanation

Let the ratio in M be A:B:W = a:b:w. Total parts = a+b+w. Lab P result (2:3:5) implies water increased. Lab Q result (6:9:10) implies water decreased. Solving the system of equations based on the volume changes leads to the ratio 6:9:11.

AI explanation

Let the initial amounts of liquids A, B, and water in sample M be x, y, and w, respectively, where x plus y plus w equals 225 ml. In lab P, the ratio of A to B remained 2 to 3, meaning x divided by y equals 2 divided by 3, so x equals 2k and y equals 3k. In lab Q, the ratio of A to B remained 6 to 9, which also simplifies to 2 to 3, confirming the initial ratio of A to B is 2 to 3. To match the 6 to 9 ratio in the 225 ml sample, the initial amounts must be A equals 60 ml and B equals 90 ml. This leaves 75 ml as the initial amount of water. When water was added for lab P, the amount of water became 100 ml to make the ratio 2 to 3 to 5 for the components. When water was evaporated for lab Q, the water became 50 ml to make the ratio 6 to 9 to 10. The initial water amount of 75 ml falls between these two values, so the true initial ratio of A to B to water is 60 to 90 to 75, which simplifies to 6 to 9 to 11.

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