Question

A person uses a mixture having parts pure 4 parts alcohol and 10 parts of spirit. After taking out some portion of the mixture, he adds equal amount of spirit to the remaining portion of the mixture such that the amount of alcohol and spirit will be in the ratio 1:3. What part of mixture is taken out?

Answer 1

Answer:

1/3 part of a mixture is taken out to give the resultant ratio as 1:3

Answer 2

The part of the mixture that was taken out was 1:8.

Step-by-step process

Given:

We are given a mixture of alcohol and spirit in the ratio of 4:10.

To find:

We need to find the part of the mixture that must be taken out such that the ratio of alcohol and spirit would be 1:3.

Solution:

The formula for final concentration is:

Final concentration= initial concentration × ( 1-x/V)

Here, x= Quantity removed from the mixutre

v= total volume for solution.

Now, the amount of alcohol initially in the solution= 4/4+10= 4/14

Amount of alcohol in the final mixture= 1/1+3= 1/4

Putting these  values in the equation, we get:

1/4= 4/14×(1-x/v)

14/16= 1-x/v

x/V= 1-14/16

x/v= 2/16

x/V= 1/8

Result:

Hence, the part of the mixture that was taken out was 1:8.

(#SPJ3)