Multiple choice

Vessels A and B contain mixtures of alcohol and water in the ratios 5 : 3 and 1 : 3 respectively . In what ratio should quantities of mixture be taken from A and B to form a new mixture in which alcohol to water is in the ratio 11 : 21?

  1. (a) 2 : 5

  2. (b) 3 : 5

  3. (c) 1 : 3

  4. (d) 2 : 3

  5. (e) 4 : 5
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Using alligation on alcohol: Vessel A has 5/8 alcohol, Vessel B has 1/4 (2/8) alcohol. Target is 11/32. (11/32 - 8/32) : (20/32 - 11/32) = 3/32 : 9/32 = 3:9 = 1:3.

AI explanation

In vessel A the fraction of alcohol is 5/8 and in vessel B it is 1/4, while the desired final mixture requires an alcohol fraction of 11/32. Using the rule of alligation with these fractions, the required ratio of the quantities from vessel A to vessel B is (1/4 minus 11/32) to (5/8 minus 11/32). This evaluates to (8/32 minus 11/32) and (20/32 minus 11/32), yielding a ratio of 3/32 to 9/32, which simplifies to 1:3.

Keep practicing — related questions