Question
Download Solution PDFThe ratio of alcohol to water in three types of drugs of equal quantity is 2 ∶ 5, 5 ∶ 9, and 8 ∶ 13 respectively. An equal quantity of all three drugs is mixed. Find the ratio of alcohol to water after mixing
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The ratio of alcohol to water in the first drug = 2 ∶ 5
The ratio of alcohol to water in the second drug = 5 ∶ 9
The ratio of alcohol to water in the third drug = 8 ∶ 13
Concept:
The ratio of alcohol to water in the mixed drug is the sum of alcohol to the sum of water in all the drugs.
Calculation:
Calculate the total alcohol and total water in the first drug.
⇒ Alcohol in first drug = 2/7, Water in first drug = 5/7
Calculate the total alcohol and total water in the second drug.
⇒ Alcohol in second drug = 5/14, Water in second drug = 9/14
Calculate the total alcohol and total water in the third drug.
⇒ Alcohol in third drug = 8/21, Water in third drug = 13/21
Sum up the total alcohol and total water from each drug.
⇒ Total alcohol = (2/7) + (5/14) + (8/21) = 43/42
⇒ Total water = (5/7) + (9/14) + (13/21) = 83/42
Therefore, the ratio of alcohol to water after mixing is 43 ∶ 83.
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