UGCNET Questions

Let the original price be 100 units for ease of calculation. A 20% increase raises the price to 120 units. A subsequent 20% decrease is applied to this new price, so the reduction is 20% of 120, which is 24. Subtracting 24 from 120 gives 96. The final price is therefore 96, which is 4 units less than the original 100, indicating a net decrease of 4%.

Option A:
Option A, 0% change, would be correct only if an increase and an equal decrease cancelled each other exactly, but this happens only when both percentages are applied to the same base value. Here the decrease is applied to an already increased price.

Option B:
Option B, 2% decrease, underestimates the net effect and would arise from a miscalculation or an incorrect averaging of percentages without considering the changed base.

Option C:
Option C accurately tracks the price through both changes and compares the final value with the initial value. The computation demonstrates that the successive operations do not cancel out but instead yield a 4% net decrease.

Option D:
Option D, 6% decrease, overstates the net reduction and cannot be derived from the multiplicative factors 1.2 and 0.8 that represent the two changes.

Let the original price be 100 units. A 10% decrease takes it to 90. A further 10% decrease is now applied to 90, resulting in a reduction of 9, so the new price is 81. The overall decrease from 100 to 81 is 19 units, which is a 19% reduction. This shows that successive equal percentage decreases do not simply add arithmetically.

Option A:
Option A, 19%, correctly reflects the multiplicative effect of two successive 10% decreases. It uses the idea that the combined factor is 0.9 × 0.9 = 0.81, corresponding to a 19% drop.

Option B:
Option B, 20%, comes from the mistaken belief that decreases add directly (10% + 10%), but this ignores that the second decrease is on an already reduced base.

Option C:
Option C, 21%, overestimates the net effect and does not correspond to the computed final value of 81.

Option D:
Option D, 25%, greatly overstates the combined impact and has no support in the actual price sequence produced by the successive reductions.

Let the original number be 100 for simplicity. Increasing it by 25% gives 100 × 1.25 = 125. Decreasing this new value by 20% means multiplying 125 by 0.8, giving 125 × 0.8 = 100. This returns exactly to the original value, so the net percentage change is 0%. Hence, Option A, 0%, correctly represents no overall increase or decrease.

Option A:
Option A, 0%, directly expresses that there is no net change in the value after both operations. It matches the calculation using multiplicative factors 1.25 and 0.8, whose product is exactly 1.

Option B:
Option B, 2% increase, would require the final value to be 102 when starting from 100, but the actual final value here is 100, so this option overstates the effect.

Option C:
Option C, 4% increase, similarly suggests a final value of 104, which is not supported by the computations of the successive changes.

Option D:
Option D, 0.5% decrease, implies a small net drop, but the actual multiplicative effect of 1.25 and 0.8 is neutral.