The percentage of alcohol initilly is .

The vat contains the beer is .

Initially the alcohol in the vat is .

The percentage of alcohol pumped into the vat at a rate of .

The percentage of alcohol pumped out the vat at a rate of .

Let  be the amount of alcohol after time .

Rate of change in percentage alcocohol is the percentage of alcohol pumped into vat minus percentage of alcohol pumped out of the vat.

Rate of change in alcohol is .

Rate of alcohol pumped into the vat is .

Rate of alcohol pumped out the vat is . 

Substitute corresponding vakues in the above equation.

Apply integration on each side.

Solve for constant .

.

Substitute and in the above equation.

Find the percentage of alcohol after an hour.

The percentage of alcohol after time is .

Here time .

Substitute and in .

Substitute   and in .

.

The percentage of alcohol after an hour is .

The percentage of alcohol after an hour is .