The 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.
Show answer & explanation
Correct answer: B
Explanation
The Correct answer is option 2 i.e. 43 : 83.
Given that
The 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.
Type 1 : The total quantity of solution = 2 + 5 = 7 units
Type 2 : The total quantity of solution = 5 + 9 = 14 units
Type 3 : The total quantity of solution = 8 + 13 = 21 units
According to the question;
The ratio of alcohol to water in the mixture;
⇒ (2/7 + 5/14 + 8/21) : (5/7 + 9/14 + 13/21)
⇒ ((12 + 15 + 16)/42) : ((30 + 27 + 26)/42)
⇒ (43/42) : (83/42)
⇒ 43 : 83
Hence, the required ratio of alcohol and water is 43 : 83.