UGCNET Questions

Profit is the difference between selling price and cost price. Here, the profit equals ₹920 − ₹800 = ₹120. The profit percentage is calculated on cost price, so it is (profit ÷ cost price) × 100 = (120 ÷ 800) × 100. This simplifies to (12 ÷ 80) × 100 = 0.15 × 100 = 15%. Therefore, the profit made is 15% of the cost price.

Option A:
Option A reflects the correct application of the profit percentage formula, using cost price as the base. The computation carefully converts the absolute profit into a relative percentage, yielding 15%, which accurately quantifies the gain.

Option B:
Option B, 12%, may result from mistakenly using the profit amount directly without proper division by the cost price. It underestimates the true rate of return on the investment.

Option C:
Option C, 10%, is even smaller and could emerge from misreading the difference or misplacing zeros, but does not match the actual ratio of 120 to 800.

Option D:
Option D, 18%, overstates the profit rate and cannot be derived from the given selling and cost prices using the standard formula.

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.