UGC NET Questions (Paper – 1)

Statement A correctly gives the standard formula for percentage change. Statement B is also true because a negative result indicates that the new value is lower than the old one. Statement E is correct as many data interpretation graphs require reading approximate values and working with reasonable approximations. Statement C is false because changing the base (denominator) alters the percentage value, and D is false since a large absolute difference can still yield a small percentage change when the base is large. Thus, A, B and E only are correct.

Option A:
Option A is incomplete because it leaves out B, which properly explains the meaning of a negative percentage change.

Option B:
Option B is correct as it combines the correct formula, the interpretation of negative change and the realistic note about approximation, while excluding C and D.

Option C:
Option C is wrong because it includes C, which wrongly claims the base value does not matter, and it omits B.

Option D:
Option D is incorrect since it contains D (false) and omits A (formula).

This option is correct because the percentage increase is calculated as (increase ÷ original value) × 100. The increase is 120 − 100 = 20. So, (20 ÷ 100) × 100 = 20%. Therefore, the price has increased by 20%.

Option A:
The increase of ₹20 over an original price of ₹100 represents 20% of the original. This is obtained directly from the formula and matches intuitive understanding. Hence, 20% is the correct percentage increase.

Option B:
A 10% increase on ₹100 would be ₹10, giving a final price of ₹110. The actual new price is ₹120, so 10% underestimates the change. Therefore, this option is wrong.

Option C:
A 15% increase would add ₹15, resulting in a price of ₹115. This still does not reach the actual new price of ₹120. Thus, 15% is not the correct percentage increase.

Option D:
A 25% increase on ₹100 would be ₹25, leading to a price of ₹125. This overshoots the given new price, so 25% is too high. Hence, this option is incorrect.

Let the two numbers be 5x and 7x. Increasing the first by 20% gives 5x × 1.2 = 6x. Decreasing the second by 20% gives 7x × 0.8 = 5.6x, which is 28x/5. The new ratio is 6x : (28x/5) = (6 × 5)x : 28x = 30x : 28x = 15:14. Therefore, 15:14 is the required new ratio.

Option A:
Option A, 4:5, would correspond to a situation where the first number becomes relatively smaller than 5x and the second number remains close to 7x. This contradicts the specified percentage changes, where the first number actually grows and the second shrinks. So 4:5 cannot arise from the given operations.

Option B:
Option B, 6:5, incorrectly suggests that the new ratio reflects only the increased numerator without accounting for the reduction in the denominator. If we take 6:5, the implied percentage change for the second number does not line up with a 20% decrease from 7x. Thus, 6:5 is not consistent with the given data.

Option C:
Option C is correct because it incorporates both the 20% increase of the first number and the 20% decrease of the second number. The algebraic simplification of the resulting expressions leads cleanly to 15:14. This ratio reflects the combined effect of both changes accurately.

Option D:
Option D, 7:6, might be guessed from the original ratio 5:7 by swapping roles and adjusting slightly, but no such transformation is described in the question. When we compute the actual new values, they do not simplify to 7:6, so this option fails the mathematical check.