The term "balanced" is applied to two different, but related subjects in aircraft performane.
A BALANCED FIELD is one in which the ASDA = TODA. This means that the stopway length is equal to the clreaway length (because ASDA = TORA + STOPWAY and TODA = TORA + CLEARWAY).
But many fields are not actually balanced. If we use the two different values of ASDA and TODA in our performance calculations, we need to carry out two separate sets of calculations. One for the ASD and one for the TODR.
But if we pretend that the two lengths are equal, we need carry out only one set of calculations. To do this we simply take the shorter of the two lengths and pretend that it applies to both ASDA and TODA.
This will reduce the maximum field limited take-off mass, but it will make the calculations easier. Provided we are not close to the field limited TOM, this slight loss of field performance is not a problem.
The second subject is that of the BALANCED TAKE-OFF which is also called the BALANCED V1 TAKE-OFF.
This is a take-off in which the ASD = TODR. Note that these are not the distances availvable, but the distances that we expect to use.
When we are not field limited we have a range of possible values for V1. The minimum value (Vgo) is the minimum speed at which we can suffer a critical engine failure and still complete the take-off within the TODA. The maximum value (Vstop) is the maximum speed at which we can abort the take-off and stop within the ASDA.
Reducing V1 within this range increases TOD but decreases ASD. Increasing V1 within this range does the opposite, increasing ASD but decreasing TOD.
A BALANCED V1 take-off is one in which ASD = TOD. This means that the overall distance is minimised. So we have maximised our safety margins within the distances avaialble.
So for the purposes of your JAR ATPL PERFexam.
Doing balanced field calculations simplyies the calcualtions.
Doing a balanced V1 take-off maximises the safety margins for any given set of distances available.