Question

Water is mixed with an alcohol-water solution with initial alcohol to water ratio a:5 such that the final solution contains 10a% alcohol. If they were mixed in the ratio 1:4, what is the value of a?​

Answer 1

Given:

Initial alcohol to water ratio a:5 such that the final solution contains 10a% alcohol.

If they were mixed in the ratio of 1:4

To find:

What is the value of a?

Solution:

Percentage concentration of alcohol in alcohol-water solution

= 100a/(a + 5) %

By Alligation method:

0%                                                100a/(a + 5) %

                                   10a%

100a/[(a + 5) - 10a]                       10a

∴ 100a/(a + 5) - 10a: 10a = 1 : 4

10/(a + 5) - 1 = 1/4

10/(a + 5) = 5/4

2(a + 5) = 1/4

8 = a + 5

a = 8 - 5

a = 3

Therefore, the value of a is 3